In http:/papers.rqgravity.net/RQGFoundations.pdf I showed how quantum
mechanics can be formulated as a theory of particles. I use this
formulation to construct qed in

http://papers.rqgravity.net/RQGQED.pdf

Imv it is important to rigorously derive cem from qed, not to find qed
by quantising cem, and to show from physical principles that the
divergences are in fact properly treated, using either lattice
regularisation or the method of Epstein and Glaser.




Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.rqgravity.net

Oh No wrote on Fri, 03 Jul 2009 15:01:58 +0000:

In http:/papers.rqgravity.net/RQGFoundations.pdf I showed how quantum
mechanics can be formulated as a theory of particles. I use this
formulation to construct qed in

http://papers.rqgravity.net/RQGQED.pdf

This is another odd article in your usual line. You start saying:

"Particle theoretic qed has been largely out of favour for more than
half a century (Feynman being a notable exception; Schweber, 1994)"

Then you write:

"Among the problems particle qed has to face are the requirement of
a positive definite norm for valid probabilities, the indefinability
of the equal point multiplication between field operators, loop
divergences, and the Landau Pole."

But none of those are the true reasons for which physicists abandoned
the particle interpretation of Dirac wave equations.

Why would physicists ignore all the work done in quantum field theory?
You critize Weinberg views [#] but why would he use inconsistent
treatments as your based in a wave-function interpretation of dirac
and KG equations? Your well-known dislike of fields as metaphysics [#]
is not a valid reason.

You assume existence of position states |x in page 2 and again in page
3, but those are not valid relativistic states.
Reason which one-particle states in relativistic quantum field theory
are *defined* using momentum and spin.

You define Dirac equation in (2.1.1). In page 3 you write:

"The Dirac equation is most readily understood as the equation of
motion for a particle in its own proper time."

Does not virtually any textbook remarks that the Dirac equation cannot
be consistently interpreted as the equation for one particle?

You work with negative energy states. In QFT energy is positive.
How do you solve stability? With Dirac sea? And for bosons?

Your constraint (3.2.1) for the potential in the interaction picture
implies (H_int)^2 = 0 by definition. But then there is not
interactions! Indeed, in page 7 you write for a Dirac solution

H_I |f = 0

and just below

H_I |f =/= 0

and next you seem to justify this with your statement about "The dual
definition of H_I". This is all confusing for me.

Next you write:

"It is usual to normal order creation and annihilation operators in
the interaction Hamiltonian"

It is usual to add normal ordering to the full Hamiltonian, including
the free term.

Page 10: "The interpretation of antiparticles as negative energy
particles". Antiparticles have not negative energy. Total energy for
free N particles and W antiparticles is

H = sqrt(m^2 + p^2) {N(p) + W(p)}

Page 11:

"The natural and simplest thing to try is to introduce a particle
with a spin index which transforms as a vector, and which is its
own antiparticle, i.e. its creation and annihilation operators
appear in the same field operator. Vector particles may have
non-zero mass, but empirical evidence is that this is not so for the
photon at the limit of experimental accuracy. Zero mass is assumed."

Do you mean you assume zero mass for the photon but it cannot be zero?

In page 14 you introduce the wavefunction KG equation. But this is
a more inconsistent wavefunction that Dirac one. KG is not more a
wavefunction equation in QFT.

Unless I am missing something in your notation, the first order
equation you give in the same page is not obtained from
differentiating KG.

In page 16 first you define P_F using H_I, but then in the computation
below you use H_I. In his book, Feynman computed the force for a
Dirac particle and obtains the standard alphaA result. He explains
the drawbacks of the derivation.

You give no explanation of why you obtain vA. In past discussions at
spf, you were using incorrect velocity operators. E.g. you refuted
that alpha was the velocity operator for a Dirac particle (but you
were wrong) and even claimed that the velocity operator was

v = p/m

http://groups.google.com/group/sci.p...e2ee67d7205cdf

which not just violates the principles of RQM

v == [H,x]

but that even disagrees with the operator for non-relativistic case!
For a non-relativistic particle in an external EM field yours is not
the velocity operator. What are you doing now?

In page 17 you talk about the Lorentz force, ignoring now the lack of
any rigorous derivation, you define therein force as

Force = d/dtau(momentum)

One of reason which we use math in physics is because words can be
ambiguous. What "momentum"? I suspect you mean the kinetic momentum pi.

But below you use P_F described by you as the "standard formula for
momentum in the presence of a field"! And you add about the formula
"but normally it is assumed, on phenomenological grounds, whereas here
it is been found theoretically." I do not know of any single treatment
where the definition of momentum was "assumed". Momentum in mechanics
has a definition and it is unique.

It is really odd that you defined force that way. In Lagrangian
mechanics force is not defined that way (but using the potential).
And in Hamiltonian mechanics force is not defined that way (because
kinetic momentum is not the momentum p for particle).

This all seems to be the same confusion you have about the difference
between F (Hamiltonian forces) and Q (Lagrangian forces).

Page 18:

"The difference is that here we use a discrete sum whereas causal
perturbation theory use a continuous switching function, and while
Scharf says (p163) the switching on and off the interaction is
unphysical, here the switching off and on of the interaction at
x_0^n = x_0^j is regarded as a physical constraint meaning that only
one interaction takes place for each particle in any instant."

(i) What have to see the unphysical switching on off of interactions
at asymptotic times with your "physical constraint"? And (ii) why do
you claim your constraint is physical?

In the same page you force energy cut-off introducing a finite lattice,
and modified propagators. This standard 'solution' whereas valid from
a phenomenological point of view, does not solve the problem of the
use of bare particles. Very odd is your "the derivation of Maxwell’s
equations shows that the bare values are physical values."

Your claim to solve the Landau Pole postulating "the minimum discrete
unit of time, chi," seems to ignore causality troubles associated to
discretizing time.

In page 19:

"In standard treatments of qed Feynman diagrams are regarded merely
as aids to calculation, not descriptions of underlying structure. In
relational quantum gravity, the perturbation expansion is
interpreted directly as a logical statement, meaning that any number
of interactions might be found taking place at any time and any
position if we were to do a measurement."

The reason which standard treatments give a formal meaning for the
diagrams is technical. Your relational quantum gravity follows from
ignoring technicalities about measurements of space and time.

I do not understand your claim

"In this interpretation, H_I(x) describes the possibility that an
interaction might be anywhere, not a quantised “matter field� which
is, in some undefined sense, everywhere."

In QFT(QED) we have e.g., fermion fields and EM fields and H_I gives
the interaction between fields.

There is many more issues in your work that deserve attention and I
avoided mathematical issues. Regarding the physics, for instance, you
have not proven relativistic locality (Due to non-analitic character
of Dirac Hamiltonian, any wavefunctions with compact support at t=0
propagate outside the light cone at latter times.), you ignore
non-interaction theorems, many-body effects...

It may be not a causality that you dislike Weinberg and other
physicists' approach, accusing field theoreticians of applying invalid
"scientific methodology" [#] whereas you have kindly words for Eugene
Stefanovich book

http://groups.google.com/group/sci.p...58d5a32bebd7f3

which I would not recommend.

Regards


[#] http://rqgravity.net/ParticlesOrFields


--
http://www.canonicalscience.org/

Thus spake Juan R. González-�lvarez
Oh No wrote on Fri, 03 Jul 2009 15:01:58 +0000:

In http:/papers.rqgravity.net/RQGFoundations.pdf I showed how quantum
mechanics can be formulated as a theory of particles. I use this
formulation to construct qed in

http://papers.rqgravity.net/RQGQED.pdf


Why would physicists ignore all the work done in quantum field theory?

I am not suggesting work on qft be ignored, since interpretation does
not alter mathematical structure.

You critize Weinberg views [#] but why would he use inconsistent
treatments as your based in a wave-function interpretation of dirac
and KG equations?

I have shown they are consistent.

You assume existence of position states |x in page 2 and again in page
3, but those are not valid relativistic states.
Reason which one-particle states in relativistic quantum field theory
are *defined* using momentum and spin.

In fact I explain why spin is needed on page 3. I have already defined
momentum states from position states in RGQ I, so it would not make
sense now to do it the other way around.

You define Dirac equation in (2.1.1). In page 3 you write:

"The Dirac equation is most readily understood as the equation of
motion for a particle in its own proper time."

Does not virtually any textbook remarks that the Dirac equation cannot
be consistently interpreted as the equation for one particle?

Such remarks are made, but simply making a remark does not make it true.
In any case, there is no problem with the non-interacting Dirac
equation, apart from the interpretation of negative energy states, and
even that is not an issue until interactions are considered.

You work with negative energy states. In QFT energy is positive.
How do you solve stability? With Dirac sea? And for bosons?

Did you not read the paper? I make no use of the Dirac sea, and I
explicitly show how the Feynman-Stueckelberg interpretation leads to the
observation of only positive energy.

Your constraint (3.2.1) for the potential in the interaction picture
implies (H_int)^2 = 0 by definition. But then there is not
interactions! Indeed, in page 7 you write for a Dirac solution
....
"The dual
definition of H_I". This is all confusing for me.

Yes, I agree this was confusing. It is also unnecessary and I have since
removed it from the paper.


Page 10: "The interpretation of antiparticles as negative energy
particles". Antiparticles have not negative energy.

It is not much good quoting a part of a sentence, or even part of a
phrase. The interpretation of antiparticles as negative energy particles
going backwards in time explains why creation and annihilation operators
are reversed, and why antiparticles appear with positive energy.

Page 11:

"The natural and simplest thing to try is to introduce a particle
with a spin index which transforms as a vector, and which is its
own antiparticle, i.e. its creation and annihilation operators
appear in the same field operator. Vector particles may have
non-zero mass, but empirical evidence is that this is not so for the
photon at the limit of experimental accuracy. Zero mass is assumed."

Do you mean you assume zero mass for the photon but it cannot be zero?

Why would zero mass be impossible?

In page 14 you introduce the wavefunction KG equation. But this is
a more inconsistent wavefunction that Dirac one. KG is not more a
wavefunction equation in QFT.

The KG equation does apply to waves and it is not inconsistent. You are
thinking of other aspects of a scalar theory, not of the KG equation
itself. It is explained in RQG I why a first order equation is needed.

Unless I am missing something in your notation, the first order
equation you give in the same page is not obtained from
differentiating KG.

Obviously not. Clearly the wave function is differentiated.

In page 16 first you define P_F using H_I, but then in the computation
below you use H_I. In his book, Feynman computed the force for a
Dirac particle and obtains the standard alphaA result. He explains
the drawbacks of the derivation.

You give no explanation of why you obtain vA. In past discussions at
spf, you were using incorrect velocity operators.

It is stated in the text that v is a classical velocity. This has
nothing to do with velocity operators, but if you refer back to the
discussions which you cite, and the parallel discussion you had with
Igor here on s.p.r. you will find that we both tried without success to
clear your confusion on the matter. I do not wish to revisit that.

In page 17 you talk about the Lorentz force, ignoring now the lack of
any rigorous derivation,

Actually I give a rigorous derivation, if you did but follow the steps.

you define therein force as

Force = d/dtau(momentum)

One of reason which we use math in physics is because words can be
ambiguous. What "momentum"? I suspect you mean the kinetic momentum pi.

But below you use P_F described by you as the "standard formula for
momentum in the presence of a field"! And you add about the formula
"but normally it is assumed, on phenomenological grounds, whereas here
it is been found theoretically." I do not know of any single treatment
where the definition of momentum was "assumed". Momentum in mechanics
has a definition and it is unique.

Definitions (or postulates) are assumed. That is why they are
definitions. They are taken as read, not proved.

It is really odd that you defined force that way. In Lagrangian
mechanics force is not defined that way (but using the potential).
And in Hamiltonian mechanics force is not defined that way (because
kinetic momentum is not the momentum p for particle).

This all seems to be the same confusion you have about the difference
between F (Hamiltonian forces) and Q (Lagrangian forces).

Actually, this was your confusion about plain old Newtonian force. There
is no need to introduce other definitions. Anyway, there is no problem
here, because the symbols are clearly defined, and the equation proved,
the Lorentz force law, is well known and understood.

Page 18:

"The difference is that here we use a discrete sum whereas causal
perturbation theory use a continuous switching function, and while
Scharf says (p163) the switching on and off the interaction is
unphysical, here the switching off and on of the interaction at
x_0^n = x_0^j is regarded as a physical constraint meaning that only
one interaction takes place for each particle in any instant."

(i) What have to see the unphysical switching on off of interactions
at asymptotic times with your "physical constraint"? And (ii) why do
you claim your constraint is physical?

I do not know how to explain better than by asking you to read
everything through again from the beginning of RQG I, since tt is a
primary purpose of these papers to explain this thoroughly and
rigorously

http://papers.rqgravity.net/RQGFoundations.pdf

In the same page you force energy cut-off introducing a finite lattice,
and modified propagators. This standard 'solution' whereas valid from
a phenomenological point of view, does not solve the problem of the
use of bare particles. Very odd is your "the derivation of Maxwell’s
equations shows that the bare values are physical values."

What I find odd is that no one else does this, since the demonstration
is really quite straightforward.

Your claim to solve the Landau Pole postulating "the minimum discrete
unit of time, chi," seems to ignore causality troubles associated to
discretizing time.

No. If you read thoroughly from the beginning you will find such
problems do not occur in this formulations.

In page 19:

"In standard treatments of qed Feynman diagrams are regarded merely
as aids to calculation, not descriptions of underlying structure. In
relational quantum gravity, the perturbation expansion is
interpreted directly as a logical statement, meaning that any number
of interactions might be found taking place at any time and any
position if we were to do a measurement."

The reason which standard treatments give a formal meaning for the
diagrams is technical. Your relational quantum gravity follows from
ignoring technicalities about measurements of space and time.

Actually I base my treatment on technicalities which are usually
ignored, starting in RQG I.


I do not understand your claim

"In this interpretation, H_I(x) describes the possibility that an
interaction might be anywhere, not a quantised “matter field� which
is, in some undefined sense, everywhere."

In QFT(QED) we have e.g., fermion fields and EM fields and H_I gives
the interaction between fields.

Whereas I have shown how to derive the same formulae without basing
anything on fields.

There is many more issues in your work that deserve attention and I
avoided mathematical issues.

It would be better if you do not, since the mathematical issues answer
most of your criticism.

Regarding the physics, for instance, you
have not proven relativistic locality (Due to non-analitic character
of Dirac Hamiltonian, any wavefunctions with compact support at t=0
propagate outside the light cone at latter times.),

I have shown the locality condition, which is all that is required.

you ignore
non-interaction theorems,


I have given a formulation in which these do not apply.

many-body effects...

Clearly I have given a many body formulation.

Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)

http://www.rqgravity.net

Oh No wrote on Mon, 13 Jul 2009 13:44:00 +0000:

Thus spake Juan R. González-�lvarez
Oh No wrote on Fri, 03 Jul 2009 15:01:58 +0000:

In http:/papers.rqgravity.net/RQGFoundations.pdf I showed how quantum
mechanics can be formulated as a theory of particles. I use this
formulation to construct qed in

http://papers.rqgravity.net/RQGQED.pdf


Why would physicists ignore all the work done in quantum field theory?

I am not suggesting work on qft be ignored, since interpretation does
not alter mathematical structure.

Your own words against QFT [#]:

"I have disagreements with the field theoretic approach on both
philosophical and mathematical grounds."

"Usually quantum electrodynamics is approached from the viewpoint that
the underlying (meta)physical structures are fields. I do not think
there is any justification for this beyond the undeniable mathematical
similarity between relativistic quantum field theory and the treatment
of quasi-particles in condensed matter physics. Field theorists argue
that, in like manner, the fundamental particles of Nature are really
quasi-particles. In my view, argument by analogy is not a valid
scientific methodology; [...] Despite considerable effort over the
years, field theory has not been able to resolve fundamental
mathematical problems in qed."

You critize Weinberg views [#] but why would he use inconsistent
treatments as your based in a wave-function interpretation of dirac and
KG equations?

I have shown they are consistent.

You have not. Read the part of my message that you sniped.

You assume existence of position states |x in page 2 and again in page
3, but those are not valid relativistic states. Reason which
one-particle states in relativistic quantum field theory are *defined*
using momentum and spin.

In fact I explain why spin is needed on page 3.

From page 3:

"There is no covariant first order equation for spinless particle, and,
following Dirac 1928, a spin index is added to the ket."

This is not true. But, moreover, solutions to Dirac equation are not kets
in QFT.

I have already defined
momentum states from position states in RGQ I, so it would not make
sense now to do it the other way around.

This avoids the issue I was really pointing out. Fortunately, as remarked
in my previous message, quantum field theory textbooks (e.g. Mandl and
Shaw, Weinberg...) do not start from a set of unphysical states as you do.

You define Dirac equation in (2.1.1). In page 3 you write:

"The Dirac equation is most readily understood as the equation of
motion for a particle in its own proper time."

Does not virtually any textbook remarks that the Dirac equation cannot
be consistently interpreted as the equation for one particle?

Such remarks are made, but simply making a remark does not make it true.

This argument can be easily inverted to see that your remarks about
textbooks are not true.

In any case, there is no problem with the non-interacting Dirac
equation, apart from the interpretation of negative energy states, and
even that is not an issue until interactions are considered.

At contrary, the equation is inconsistent even for a single electron in a
positive energy state. In QFT, the free Dirac equation is not a wave
equation because that reason.

You work with negative energy states. In QFT energy is positive. How do
you solve stability? With Dirac sea? And for bosons?

Did you not read the paper? I make no use of the Dirac sea, and I
explicitly show how the Feynman-Stueckelberg interpretation leads to the
observation of only positive energy.

Unless you cannot read, the Stückelberg & Feynman interpretation works
with hypothetical particles in states of negative energy, but particles
have always positive energy in QFT because stability and consistency
issues.

Your constraint (3.2.1) for the potential in the interaction picture
implies (H_int)^2 = 0 by definition. But then there is not interactions!
Indeed, in page 7 you write for a Dirac solution
...
"The dual
definition of H_I". This is all confusing for me.

Yes, I agree this was confusing. It is also unnecessary and I have since
removed it from the paper.

I see you also removed your pair of inconsistent equations

H_I |f = 0

H_I |f =/= 0

It would be a good thing if you remove the entire paper :-D

Page 10: "The interpretation of antiparticles as negative energy
particles". Antiparticles have not negative energy.

It is not much good quoting a part of a sentence, or even part of a
phrase. The interpretation of antiparticles as negative energy particles
going backwards in time explains why creation and annihilation operators
are reversed, and why antiparticles appear with positive energy.

The phrase "particles going backwards in time" may be one of most
meaningless phrases in physics ever and this has little to see with
quoting all or part of a sentence/phrase.

In QFT all particles/antiparticles have positive energy and move *forward*
in time because consistency issues.

Among the parts of my message you sniped, I wrote:

"Total energy for free N particles and W antiparticles is

H = sqrt(m^2 + p^2) {N(p) + W(p)}"

Even in latter times Stuckelberg worked a theory (Stuckelberg theory)
where *all* particles/antiparticles move *forward* in time and the
Hamiltonian is positive.

Page 11:

"The natural and simplest thing to try is to introduce a particle
with a spin index which transforms as a vector, and which is its own
antiparticle, i.e. its creation and annihilation operators appear in
the same field operator. Vector particles may have non-zero mass, but
empirical evidence is that this is not so for the photon at the limit
of experimental accuracy. Zero mass is assumed."

Do you mean you assume zero mass for the photon but it cannot be zero?

Why would zero mass be impossible?

Is that a "yes" or a "no" to my question about the quote in page 11?

In page 14 you introduce the wavefunction KG equation. But this is a
more inconsistent wavefunction that Dirac one. KG is not more a
wavefunction equation in QFT.

The KG equation does apply to waves and it is not inconsistent.

Thanks by the laugh. The equation that applies to classical waves is the
classical wave equation *not* the KG equation for wavefunctions.

You are
thinking of other aspects of a scalar theory, not of the KG equation
itself. It is explained in RQG I why a first order equation is needed.

I encourage you to learn, from textbooks, the differences between the
classical wave equation of EM, the wavefunction KG equation of RQM, and
the field KG equation in QFT before doing such claims in a paper.

Unless I am missing something in your notation, the first order equation
you give in the same page is not obtained from differentiating KG.

Obviously not. Clearly the wave function is differentiated.

After your confirmation this was not a notation issue, it is obvious you
do not know you are doing.

In page 16 first you define P_F using H_I, but then in the computation
below you use H_I. In his book, Feynman computed the force for a Dirac
particle and obtains the standard alphaA result. He explains the
drawbacks of the derivation.

You give no explanation of why you obtain vA. In past discussions at
spf, you were using incorrect velocity operators.

It is stated in the text that v is a classical velocity. This has
nothing to do with velocity operators,

Which confirms that you merely wrote a final result without actually
showing that the result follows from the underlying theory.

Feynman, in his treatment of QED, gave us an attempt to derive the
classical result from Dirac theory, explaining some of the drawbacks of
the derivation.

but if you refer back to the
discussions which you cite, and the parallel discussion you had with
Igor here on s.p.r. you will find that we both tried without success to
clear your confusion on the matter. I do not wish to revisit that.

It is rather unfair that you make assertions of this kind without even
giving links to my supposed "confusions on the matter".

It is still more unfair when you snip the link to my corrections of your
nonsensical messages. For fairness I reintroduce again the link

http://groups.google.com/group/sci.p...undations/msg/
fce2ee67d7205cdf

where I explained to you that *your* (v = p/m) is NOT the velocity
operator for a Dirac particle.

In fact, *your* (v = p/m) is not even the velocity operator for a
non-relativistic particle in a EM field, as explained in QM textbooks.

Your work is that inconsistent!

In page 17 you talk about the Lorentz force, ignoring now the lack of
any rigorous derivation,

Actually I give a rigorous derivation, if you did but follow the steps.

You give no derivation, less something rigorous.

Feynman, in his treatment of QED, gave us an attempt to derive the
classical Lorentz force from the Dirac theory plus EM fields. He correctly
points that the final result is not the Lorentz force law, explaining some
of the difficulties.

It is, of course, possible to give a quantum foundation for the Lorentz
law, but this cannot be done in the framework of Dirac wavefunction
theory.

you define therein force as

Force = d/dtau(momentum)

One of reason which we use math in physics is because words can be
ambiguous. What "momentum"? I suspect you mean the kinetic momentum pi.

But below you use P_F described by you as the "standard formula for
momentum in the presence of a field"! And you add about the formula "but
normally it is assumed, on phenomenological grounds, whereas here it is
been found theoretically." I do not know of any single treatment where
the definition of momentum was "assumed". Momentum in mechanics has a
definition and it is unique.

Definitions (or postulates) are assumed. That is why they are
definitions. They are taken as read, not proved.

That was not the point. The point is that you state, as quoted above that
the formulae for the momentum in the presence of a field is assumed on
phenomenological grounds, but this is not true: the formulae for momentum
follows from its theoretical definition.

It is really odd that you defined force that way. In Lagrangian
mechanics force is not defined that way (but using the potential). And
in Hamiltonian mechanics force is not defined that way (because kinetic
momentum is not the momentum p for particle).

This all seems to be the same confusion you have about the difference
between F (Hamiltonian forces) and Q (Lagrangian forces).

Actually, this was your confusion about plain old Newtonian force. There
is no need to introduce other definitions.

This is a new instance of your inability to understand why modern
mechanics textbooks (Goldstein, Ukawia...) define both F and Q and
when/how each force is used in the respective Hamiltonian or Lagrangian
equations of motion.

Another gems from you include:

"The real misunderstanding is to think that classical mechanics, or
indeed classical electrodynamics, can be defined from the Hamiltonian
formulation [...]"

"This is because Hamiltonian mechanics does not directly describe
empirical quantities like force. Redefining force to be something
different from what it is makes a nonsense of empirical science."

Anyway, there is no problem
here, because the symbols are clearly defined, and the equation proved,
the Lorentz force law, is well known and understood.

The problem remains because you confound concepts.

If by "Force" in your equation

Force = d/dtau(momentum)

you mean Q, then "momentum" may be the kinetic momentum (usually denoted
by symbol pi) and different from the momentum of the particle in the
presence of a field (usually denoted by p).

As quoted above you interpret "momentum" in your equation as being your
P_F, which is defined by you as the "standard formula for momentum in the
presence of a field"!

But if the right hand side of the equation contains the "momentum in the
presence of a field", then the left hand side cannot be the force Q but
the force F!

As explained in textbooks (Goldstein, Ukawia...) the difference between pi
and p is reproduced in the definition for force Q.

Page 18:

"The difference is that here we use a discrete sum whereas causal
perturbation theory use a continuous switching function, and while
Scharf says (p163) the switching on and off the interaction is
unphysical, here the switching off and on of the interaction at
x_0^n = x_0^j is regarded as a physical constraint meaning that only
one interaction takes place for each particle in any instant."

(i) What have to see the unphysical switching on off of interactions at
asymptotic times with your "physical constraint"? And (ii) why do you
claim your constraint is physical?

I do not know how to explain better than by asking you to read
everything through again from the beginning of RQG I, since tt is a
primary purpose of these papers to explain this thoroughly and
rigorously

http://papers.rqgravity.net/RQGFoundations.pdf

This was already presented by you in this same group and revised.

In the same page you force energy cut-off introducing a finite lattice,
and modified propagators. This standard 'solution' whereas valid from a
phenomenological point of view, does not solve the problem of the use of
bare particles. Very odd is your "the derivation of Maxwell’s equations
shows that the bare values are physical values."

What I find odd is that no one else does this, since the demonstration
is really quite straightforward.

Scientists are that kind of weird people ignoring 'demonstrations' as
those by you.

Your claim to solve the Landau Pole postulating "the minimum discrete
unit of time, chi," seems to ignore causality troubles associated to
discretizing time.

No. If you read thoroughly from the beginning you will find such
problems do not occur in this formulations.

Maybe you could cite a specific page.

In page 19:

"In standard treatments of qed Feynman diagrams are regarded merely
as aids to calculation, not descriptions of underlying structure. In
relational quantum gravity, the perturbation expansion is interpreted
directly as a logical statement, meaning that any number of
interactions might be found taking place at any time and any position
if we were to do a measurement."

The reason which standard treatments give a formal meaning for the
diagrams is technical. Your relational quantum gravity follows from
ignoring technicalities about measurements of space and time.

Actually I base my treatment on technicalities which are usually
ignored, starting in RQG I.

Your "RQG I" paper also ignores technicalities about measurements of space
and time and makes the same invalid statements about Feynman diagrams.

I do not understand your claim

"In this interpretation, H_I(x) describes the possibility that an
interaction might be anywhere, not a quantised “matter field� which
is, in some undefined sense, everywhere."

In QFT(QED) we have e.g., fermion fields and EM fields and H_I gives the
interaction between fields.

Whereas I have shown how to derive the same formulae without basing
anything on fields.

Could you maintain the discussion on-topic, replying the issues instead
ignoring them giving us continuous advertising?

There is many more issues in your work that deserve attention and I
avoided mathematical issues.

It would be better if you do not, since the mathematical issues answer
most of your criticism.

Regarding the physics, for instance, you
have not proven relativistic locality (Due to non-analitic character of
Dirac Hamiltonian, any wavefunctions with compact support at t=0
propagate outside the light cone at latter times.),

I have shown the locality condition, which is all that is required.

This is all one requires in QFT, which does not use your unphysical
relativistic states neither propagate Dirac wavefunctions.

You are once more again simply ignoring any technical defect in your work.

you ignore
non-interaction theorems,


I have given a formulation in which these do not apply.

Not in the paper presented to us.

many-body effects...

Clearly I have given a many body formulation.

Dirac did clear in his work that his own wavefunction theory was not valid
for many-body effects. Weinberg remarks in his textbook that QFT cannot
give a complete and satisfactory treatment of many-body effects. And
Landau did a similar remark. Stuckelberg went beyond and formulated an
explicit many-body theory (named the Stuckelberg theory) which avoids some
of the deficiencies in your RQG theory.

It would be time-demanding to list here all the deficiencies of your
invalid RQG theory. Moreover, there is not real need, since the theory is
not even suitable for studying simple systems as free particles.

Regards.

[#] http://rqgravity.net/ParticlesOrFields


--
http://www.canonicalscience.org/