"Bill Hobba" wrote in message news:...

Woops guys - sorry I hit the send by accident before I completed the post.


"Gregory L. Hansen" wrote in message
...
In article ,
Bill Hobba wrote:

"Gregory L. Hansen" wrote in message
...
In article ,
Bill Hobba wrote:


What collapse of the wavefunction? That's part of the interpretation
where we try to explain the measurement of quantum systems by people
that
don't obey the laws of quantum mechanics.

Very true - consistent histories for example consideres it simply a
mathematical procedure for calculating conditional probabilities that can
be
arrived at by other means. Primary state diffusion considers it an
actual
physical process. Interestingly primary state diffusion is
experimentally
distinguishable from other interpretations which IMHO is allays a big
plus.

Primary state diffusion is a new one to me.


Check out
http://arxiv.org/abs/quant-ph/9508021

It may have been experimentally disproved by now. I doubt it has been
experimentally proved since that would be big news.


Now deBroglie's relation, that has consequences that I think are rarely
appreciated. Mention wave-particle duality, and any bright student can
immediately begin to think of quantum mechanics as just another wave
mechanics. But p=h*lambda, relates a particular p to a particular
lambda.
That means if a radiation field with wavelength lambda interacts with a
particle, you'll transfer momentum p=0 or p=h*lambda, and nothing
in-between. There's the photon, particle-like behavior without ever
needing to introduce particles. QFT texts always seem to introduce a
photon propagator ex nihilo, maybe with some comment about Green's
functions, but I don't think I've ever seen them relate it to that
relation found on page 3 of a second-year physics book.

IMHO the propagator is simply a mathematical consequence of the path
integral formalism. If Z is the path integral then it can be written in
the
form Z(J) = F(x) exp iW(J) then W(J) can be written in terms of the
propagator. To me it is simply a usefull mathematical device.

I hardly think it's fair to sa that it's a mathematical consequence of
the
path integral formalism since propagators were used before the path
integral formalism was formulated.

Sure Greens functions and all that sort of stuff from the tools of
mathematical physics. But I don't quite follow your reasoning of why it
makes it more than a mathematical tool.


A Green's function G(x,y) is the action of the field at point y due to a
source at point x, where the points include time. Then you can integrate
over the source points. They've been used in field theories before
quantum mechanics existed. When you explore particle interactions you
want the momentum space representatin, G(p,q), which tells you the
momentum transfers to the particle (i.e. the energy and the scattering
angle). In a classical problem when you integrate over the momenta you
can interpret that as "a little bit of this momentum, and a little bit of
that momentum". In the quantum problem the interpretation would be more
like "all of this momentum, or all of that momentum". The "all of" part
is deBroglie's relation, the "or" part is the superposition of states.
And that, I think, gets us to what quantum field theory is about, without
reference to a particular mathematical formalism.

I think QFT is about reconciling QM with relativity. To do that we must
treat everything as field - sometimes called the method of second
quantisiation. I am not the only one who thinks so - Weinberg wrote a whole
book about it viewed that way. I have a copy, have read it, but have not
studied it in detail.

Thanks
Bill


--
"He who only sees business in business is a fool."

Bill Hobba wrote:

[snip]

I think QFT is about reconciling QM with relativity. To do that we must
treat everything as field - sometimes called the method of second
quantisiation...

You think, or you know? hahahahahahahahah

Mike


Thanks
Bill


--
"He who only sees business in business is a fool."

In article ,
Bill Hobba wrote:

"Bill Hobba" wrote in message news:...

Woops guys - sorry I hit the send by accident before I completed the post.

You silly goose.

Now deBroglie's relation, that has consequences that I think are rarely
appreciated. Mention wave-particle duality, and any bright student can
immediately begin to think of quantum mechanics as just another wave
mechanics. But p=h*lambda, relates a particular p to a particular
lambda.
That means if a radiation field with wavelength lambda interacts with a
particle, you'll transfer momentum p=0 or p=h*lambda, and nothing
in-between. There's the photon, particle-like behavior without ever
needing to introduce particles. QFT texts always seem to introduce a
photon propagator ex nihilo, maybe with some comment about Green's
functions, but I don't think I've ever seen them relate it to that
relation found on page 3 of a second-year physics book.

IMHO the propagator is simply a mathematical consequence of the path
integral formalism. If Z is the path integral then it can be written in
the
form Z(J) = F(x) exp iW(J) then W(J) can be written in terms of the
propagator. To me it is simply a usefull mathematical device.

I hardly think it's fair to sa that it's a mathematical consequence of
the
path integral formalism since propagators were used before the path
integral formalism was formulated.

Sure Greens functions and all that sort of stuff from the tools of
mathematical physics. But I don't quite follow your reasoning of why it
makes it more than a mathematical tool.

That makes it something that didn't originate with the path integral
formulation.



A Green's function G(x,y) is the action of the field at point y due to a
source at point x, where the points include time. Then you can integrate
over the source points. They've been used in field theories before
quantum mechanics existed. When you explore particle interactions you
want the momentum space representatin, G(p,q), which tells you the
momentum transfers to the particle (i.e. the energy and the scattering
angle). In a classical problem when you integrate over the momenta you
can interpret that as "a little bit of this momentum, and a little bit of
that momentum". In the quantum problem the interpretation would be more
like "all of this momentum, or all of that momentum". The "all of" part
is deBroglie's relation, the "or" part is the superposition of states.
And that, I think, gets us to what quantum field theory is about, without
reference to a particular mathematical formalism.

I think QFT is about reconciling QM with relativity. To do that we must
treat everything as field - sometimes called the method of second
quantisiation. I am not the only one who thinks so - Weinberg wrote a whole
book about it viewed that way. I have a copy, have read it, but have not
studied it in detail.

Except that there are also non-relativistic QFTs, both non-relativistic
QED (I have a book about that one, I think by Barut) and field theories
used in the many-body problems studied by condensed matter physicists.
And you can certainly do relativistic QM with wave equations (Greiner
wrote a book on it, and many of the introductory QM books have a chapter
on the Dirac equation).

A problem with relativistic QM with wave equations is that particle number
isn't conserved when you go relativistic. I was pretty happy to learn
that it's not something put in by hand-- you can't avoid it. That's not
too much of a problem when it's approximately conserved, but becomes more
of a problem near heavy nuclei. And then you go to high energy
accelerators and all Hell breaks loose. Second quantization is about
allowing particle number to change without having to write a new equation
for each unique case. Yes, that's useful in the relativistic problem,
but that doesn't make it "about" reconciling QM with relativity. It's
also useful, e.g. for creating particle-hole pairs in condensed matter
theory.

I guess when you second quantize the system you have a field theory, but
it seems that people who just want to allow particle number to change
don't think in terms of a field theory. Quantum field theory proper
begins with a Lagrangian density and transformation rules. The
Lagrangian density is used to define the stress-energy tensor, and from
that you can pick out energy, momentum, and angular momentum. So far
it's not quantum, it's just a field theory. You could have been doing
classical electromagnetism the same way. You quantize the fields exactly
once and get a quantum field theory. Think of it as Quantization
Mark II, not the second time you quantize it. Quantum field theory is
called quantum field theory because it's a theory of fields. In nice
spacetimes it has a particle interpretation, but the particle
interpretation isn't a necessary part of it. As I'd said above,
deBroglie's relation enforces some particle-like behavior, like a sudden
and finite momentum transfer as if two billiard balls collided. But you
can think of that as a transfer of momentum between fields rather than
interacting virtual particles. (See Greiner's book Field Quantization,
and Wald's book on black hole thermodynamics.)

Quantum field theory is about applying quantum mechanics to fields. You
could apply it to continuous fluids, too (not composed of discrete
particles). Quantum mechanics is a totally general mechanics, like the
others, and isn't restricted to just one or two specific assumptions about
What Stuff Is Made Of.
--
"Not that there's anything wrong with just lying around on your back. In
its way, rotting is interesing too... It's just that there are other ways
to spend your time as a cadaver." -- Mary Roach, "Stiff", 2003.

"Gregory L. Hansen" wrote in message
...
In article ,
Bill Hobba wrote:

"Bill Hobba" wrote in message news:...

Woops guys - sorry I hit the send by accident before I completed the post.

You silly goose.

Now deBroglie's relation, that has consequences that I think are
rarely
appreciated. Mention wave-particle duality, and any bright student
can
immediately begin to think of quantum mechanics as just another wave
mechanics. But p=h*lambda, relates a particular p to a particular
lambda.
That means if a radiation field with wavelength lambda interacts with
a
particle, you'll transfer momentum p=0 or p=h*lambda, and nothing
in-between. There's the photon, particle-like behavior without ever
needing to introduce particles. QFT texts always seem to introduce a
photon propagator ex nihilo, maybe with some comment about Green's
functions, but I don't think I've ever seen them relate it to that
relation found on page 3 of a second-year physics book.

IMHO the propagator is simply a mathematical consequence of the path
integral formalism. If Z is the path integral then it can be written
in
the
form Z(J) = F(x) exp iW(J) then W(J) can be written in terms of the
propagator. To me it is simply a usefull mathematical device.

I hardly think it's fair to sa that it's a mathematical consequence of
the
path integral formalism since propagators were used before the path
integral formalism was formulated.

Sure Greens functions and all that sort of stuff from the tools of
mathematical physics. But I don't quite follow your reasoning of why it
makes it more than a mathematical tool.

That makes it something that didn't originate with the path integral
formulation.

Ah yes - I see your point.




A Green's function G(x,y) is the action of the field at point y due to
a
source at point x, where the points include time. Then you can
integrate
over the source points. They've been used in field theories before
quantum mechanics existed. When you explore particle interactions you
want the momentum space representatin, G(p,q), which tells you the
momentum transfers to the particle (i.e. the energy and the scattering
angle). In a classical problem when you integrate over the momenta you
can interpret that as "a little bit of this momentum, and a little bit
of
that momentum". In the quantum problem the interpretation would be
more
like "all of this momentum, or all of that momentum". The "all of"
part
is deBroglie's relation, the "or" part is the superposition of states.
And that, I think, gets us to what quantum field theory is about,
without
reference to a particular mathematical formalism.

I think QFT is about reconciling QM with relativity. To do that we must
treat everything as field - sometimes called the method of second
quantisiation. I am not the only one who thinks so - Weinberg wrote a
whole
book about it viewed that way. I have a copy, have read it, but have not
studied it in detail.

Except that there are also non-relativistic QFTs, both non-relativistic
QED (I have a book about that one, I think by Barut) and field theories
used in the many-body problems studied by condensed matter physicists.
And you can certainly do relativistic QM with wave equations (Greiner
wrote a book on it, and many of the introductory QM books have a chapter
on the Dirac equation).

Good point.


A problem with relativistic QM with wave equations is that particle number
isn't conserved when you go relativistic. I was pretty happy to learn
that it's not something put in by hand-- you can't avoid it. That's not
too much of a problem when it's approximately conserved, but becomes more
of a problem near heavy nuclei. And then you go to high energy
accelerators and all Hell breaks loose. Second quantization is about
allowing particle number to change without having to write a new equation
for each unique case. Yes, that's useful in the relativistic problem,
but that doesn't make it "about" reconciling QM with relativity. It's
also useful, e.g. for creating particle-hole pairs in condensed matter
theory.

I guess when you second quantize the system you have a field theory, but
it seems that people who just want to allow particle number to change
don't think in terms of a field theory. Quantum field theory proper
begins with a Lagrangian density and transformation rules.

Yes.

Thanks
Bill

The
Lagrangian density is used to define the stress-energy tensor, and from
that you can pick out energy, momentum, and angular momentum. So far
it's not quantum, it's just a field theory. You could have been doing
classical electromagnetism the same way. You quantize the fields exactly
once and get a quantum field theory. Think of it as Quantization
Mark II, not the second time you quantize it. Quantum field theory is
called quantum field theory because it's a theory of fields. In nice
spacetimes it has a particle interpretation, but the particle
interpretation isn't a necessary part of it. As I'd said above,
deBroglie's relation enforces some particle-like behavior, like a sudden
and finite momentum transfer as if two billiard balls collided. But you
can think of that as a transfer of momentum between fields rather than
interacting virtual particles. (See Greiner's book Field Quantization,
and Wald's book on black hole thermodynamics.)

Quantum field theory is about applying quantum mechanics to fields. You
could apply it to continuous fluids, too (not composed of discrete
particles). Quantum mechanics is a totally general mechanics, like the
others, and isn't restricted to just one or two specific assumptions about
What Stuff Is Made Of.
--
"Not that there's anything wrong with just lying around on your back. In
its way, rotting is interesing too... It's just that there are other ways
to spend your time as a cadaver." -- Mary Roach, "Stiff", 2003.