Hello to all:

I have over the past few months been studying Zee's excellent book "QFT
in a Nutshell." I had some questions regarding the degrees of freedom
for a Dirac spinor.

Just as the Klein-Gordon equation for a non-zero mass projects one
unphysical degree of freedom out of a four-vector potential leaving it
with three degrees of freedom (two transverse, one longitudinal), the
Dirac equation for a non-zero mass projects two degrees of freedom out
of a four-spinor wavefunction leaving it with two degrees of freedom
(spins up and down).

We also know that to give mass to a massless vector boson, one starts
with a four-vector potential with two transverse degrees of freedom, and
adds a third longitudinal degree freedom by "swallowing" a
Nambu-Goldstone scalar. Importantly, such a mechanism is also
*predictive* of the mass.

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in detail
and arrive at the right masses. But, my question is whether this line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
_____________________________
Jay R. Yablon
Email:

Jay R. Yablon wrote:
Hello to all:

I have over the past few months been studying Zee's excellent book "QFT
in a Nutshell." I had some questions regarding the degrees of freedom
for a Dirac spinor.

Just as the Klein-Gordon equation for a non-zero mass projects one
unphysical degree of freedom out of a four-vector potential leaving it
with three degrees of freedom (two transverse, one longitudinal), the
Dirac equation for a non-zero mass projects two degrees of freedom out
of a four-spinor wavefunction leaving it with two degrees of freedom
(spins up and down).

We also know that to give mass to a massless vector boson, one starts
with a four-vector potential with two transverse degrees of freedom, and
adds a third longitudinal degree freedom by "swallowing" a
Nambu-Goldstone scalar. Importantly, such a mechanism is also
*predictive* of the mass.

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in detail
and arrive at the right masses. But, my question is whether this line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
_____________________________
Jay R. Yablon
Email:

I just replied to you at sci.physics.research, but I may as well repost
since it will take some time to moderate there.

Klein-Gordon doesn't project out a degree of freedom associated with a
component, it ensures the momentum is on the mass shell. Any component
of any field satisfies that equation, including a spinor field. The
'projection' for a massive 4-vector field is given by something else
called the Proca equations.

1) yes
2) In the standard model you do start with massless spinors, but you
have the mechanism wrong. Read further in Zee.

Hope that helps,

Dan
hidden-irony.blogspot.com

Jay R. Yablon wrote:
Hello to all:

I have over the past few months been studying Zee's excellent book "QFT
in a Nutshell." I had some questions regarding the degrees of freedom
for a Dirac spinor.

Just as the Klein-Gordon equation for a non-zero mass projects one
unphysical degree of freedom out of a four-vector potential leaving it
with three degrees of freedom (two transverse, one longitudinal), the
Dirac equation for a non-zero mass projects two degrees of freedom out
of a four-spinor wavefunction leaving it with two degrees of freedom
(spins up and down).

We also know that to give mass to a massless vector boson, one starts
with a four-vector potential with two transverse degrees of freedom, and
adds a third longitudinal degree freedom by "swallowing" a
Nambu-Goldstone scalar. Importantly, such a mechanism is also
*predictive* of the mass.

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in detail
and arrive at the right masses. But, my question is whether this line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
_____________________________
Jay R. Yablon
Email:

I just replied to you at sci.physics.research, but I may as well repost
since it will take some time to moderate there.

Klein-Gordon doesn't project out a degree of freedom associated with a
component, it ensures the momentum is on the mass shell. Any component
of any field satisfies that equation, including a spinor field. The
'projection' for a massive 4-vector field is given by something else
called the Proca equations.

1) yes
2) In the standard model you do start with massless spinors, but you
have the mechanism wrong. Read further in Zee.

Hope that helps,

Dan
hidden-irony.blogspot.com

Jay R. Yablon wrote:
Hello to all:

I have over the past few months been studying Zee's excellent book "QFT
in a Nutshell." I had some questions regarding the degrees of freedom
for a Dirac spinor.

Just as the Klein-Gordon equation for a non-zero mass projects one
unphysical degree of freedom out of a four-vector potential leaving it
with three degrees of freedom (two transverse, one longitudinal), the
Dirac equation for a non-zero mass projects two degrees of freedom out
of a four-spinor wavefunction leaving it with two degrees of freedom
(spins up and down).

We also know that to give mass to a massless vector boson, one starts
with a four-vector potential with two transverse degrees of freedom, and
adds a third longitudinal degree freedom by "swallowing" a
Nambu-Goldstone scalar. Importantly, such a mechanism is also
*predictive* of the mass.

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in detail
and arrive at the right masses. But, my question is whether this line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
_____________________________
Jay R. Yablon
Email:

I'm sorry if this is double posted. Google isn't treating me right.

It's the Proca equations, not the Klein-Gordon, that eliminates one of
the degrees of freedom of a massive vector field. Klein-Gordon just
puts the momentum on the mass shell, and it's satisfied by any
component of any field.

1) yes
2) In the standard model you do start with massless fermions, but you
have the mechanism wrong. Read further in Zee.

Hope this helps,

Dan
http://hidden-irony.blogspot.com

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed
of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and
have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in
detail
and arrive at the right masses. But, my question is whether this
line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
.. . .

Klein-Gordon doesn't project out a degree of freedom associated with a
component, it ensures the momentum is on the mass shell. Any
component
of any field satisfies that equation, including a spinor field. The
'projection' for a massive 4-vector field is given by something else
called the Proca equations.

1) yes
2) In the standard model you do start with massless spinors, but you
have the mechanism wrong. Read further in Zee.

Hope that helps,

Dan
hidden-irony.blogspot.com

Dan, thanks for your reply. Perhaps I need to clarify my question,
because the emphasis I am suggesting is on "a *predictive* mechanism for
Fermion masses "

When a vector boson mass is revealed because a Nambu / Goldstone scalar
is swallowed by a vector potential, that mass is *predicted" because it
is a function *only* of strength of known dimensionless running
couplings -- in the case of the W and Z bosons of electroweak theory,
the electromagnetic and weak isospin running couplings.

I am familiar with the standard model for giving mass to fermions, but
the mass values arrived at are *arbitrary* because the (Yukawa type, I
believe?) couplings do not relate to any known couplings like the
electromagnetic and/or weak and/or strong (though one may suspect that
they should, we just don't know how). This is a well-known limitation
of the standard model, because the couplings are made proportional "by
hand" to the experimentally-observed fermion mass values but the fermion
mass values are not in any way predicted as are the W and Z boson
masses. Not to mention that we have no clue as to why nature replicates
fermions into three mass-distinguished generations and so far can do
nothing more than play games with masses and Cabibbo-type mixing angles.
One would have to at least suspect that we will never have a true answer
as to why the fermions have the masses they do until we understand why
nature has dealt us the Fermion generation redundancy for which nobody
has ever uncovered a theoretical necessity.

So, what I am asking is whether the mechanism I am suggesting with a
mutual swallowing / sharing of degrees of freedom between a pure R and a
pure L Weyl spinor might make some sense in thinking about a
*predictive* mechanism for revealing fermion masses which, by definition
as something predictive, would go beyond the standard model to new
territory. I am not asking if this is "right" for sure because we can't
know that without the details. Just asking if this seems to be a
sensible way to think about this particle physics research problem (or
at least part of this problem) for which nobody today has any sure
answers.

Jay.

Jay R. Yablon wrote:
Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed
of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and
have
these two Weyl spinors "swallow" up the degrees of freedom from one
another (yes, I know that sounds obscene ;-) ) yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in
detail
and arrive at the right masses. But, my question is whether this
line
of inquiry makes basic theoretical sense at the outset?

Thanks,

Jay.
. . .

Klein-Gordon doesn't project out a degree of freedom associated with a
component, it ensures the momentum is on the mass shell. Any
component
of any field satisfies that equation, including a spinor field. The
'projection' for a massive 4-vector field is given by something else
called the Proca equations.

1) yes
2) In the standard model you do start with massless spinors, but you
have the mechanism wrong. Read further in Zee.

Hope that helps,

Dan
hidden-irony.blogspot.com

Dan, thanks for your reply. Perhaps I need to clarify my question,
because the emphasis I am suggesting is on "a *predictive* mechanism for
Fermion masses "

When a vector boson mass is revealed because a Nambu / Goldstone scalar
is swallowed by a vector potential, that mass is *predicted" because it
is a function *only* of strength of known dimensionless running
couplings -- in the case of the W and Z bosons of electroweak theory,
the electromagnetic and weak isospin running couplings.

I am familiar with the standard model for giving mass to fermions, but
the mass values arrived at are *arbitrary* because the (Yukawa type, I
believe?) couplings do not relate to any known couplings like the
electromagnetic and/or weak and/or strong (though one may suspect that
they should, we just don't know how). This is a well-known limitation
of the standard model, because the couplings are made proportional "by
hand" to the experimentally-observed fermion mass values but the fermion
mass values are not in any way predicted as are the W and Z boson
masses. Not to mention that we have no clue as to why nature replicates
fermions into three mass-distinguished generations and so far can do
nothing more than play games with masses and Cabibbo-type mixing angles.
One would have to at least suspect that we will never have a true answer
as to why the fermions have the masses they do until we understand why
nature has dealt us the Fermion generation redundancy for which nobody
has ever uncovered a theoretical necessity.

So, what I am asking is whether the mechanism I am suggesting with a
mutual swallowing / sharing of degrees of freedom between a pure R and a
pure L Weyl spinor might make some sense in thinking about a
*predictive* mechanism for revealing fermion masses which, by definition
as something predictive, would go beyond the standard model to new
territory. I am not asking if this is "right" for sure because we can't
know that without the details. Just asking if this seems to be a
sensible way to think about this particle physics research problem (or
at least part of this problem) for which nobody today has any sure
answers.

Jay.

Well, it's very sensible in a certain way, because mass (at least at
the field equation level) can be thought of as a coupling between the
pure left and right fields. What you're vaguely saying sounds very
similar to what actually occurs in the standard model. But look at the
chapter on the Higgs mechanism again (the "swallowing"), it depends
crucially on the properties of the gauge field. We need those extra
parameters which aren't predictive to give the fermions mass too, we
can't get it 'for free' with the Higgs mechanism.

But if you're suggesting something completely different and radical,
and I don't think so, you should get someone else to answer.

Dan
hidden-irony.blogspot.com

$$ Virtually between w & z bosons at-a-distance.
$$ Question:
$$ What is ..THEORETiCALLY, *in BETWEEN* ADjACENT w or z bozons?
$$
$$ Answer:
$$ A *ViRTUAL SPACE* is in BETWEEN adjacent ViRTUAL *PARTicles".
$$
$$ Distinguish a "degree-of-freedom", from "NOthing-at-a-distance".

Jay R. Yablon wrote: Questions:
1) Is it proper,

2) In rough analogy to how boson mass is "revealed,"

these two Weyl spinors "swallow"

Jay.
. . .

Klein-Gordon doesn't project out a degree of freedom

Hope that helps,

Dan

When a vector boson mass is revealed because a Nambu / Goldstone scalar
is swallowed

One would have to at least suspect that we will never have a true answer
as to why the fermions have the masses they do until we understand why
nature has dealt us the Fermion generation redundancy for which nobody
has ever uncovered a theoretical necessity.

So, what I am asking is whether the mechanism I am suggesting with a
mutual swallowing / sharing of degrees of freedom between a pure R and a
pure L Weyl spinor might make some sense in thinking about a
*predictive* mechanism for revealing fermion masses which, by definition
as something predictive, would go beyond the standard model to new
territory. I am not asking if this is "right" for sure because we can't
know that without the details. Just asking if this seems to be a
sensible way to think about this particle physics research problem (or
at least part of this problem) for which nobody today has any sure
answers.

$$ What exactly are you asking? snicker

Jay.
Dirac Spinors and Degrees of Freedom. END of POST.

Jay R. Yablon wrote:
Hello to all:

I have over the past few months been studying Zee's excellent book "QFT
in a Nutshell." I had some questions regarding the degrees of freedom
for a Dirac spinor.

Just as the Klein-Gordon equation for a non-zero mass projects one
unphysical degree of freedom out of a four-vector potential leaving it
with three degrees of freedom (two transverse, one longitudinal), the
Dirac equation for a non-zero mass projects two degrees of freedom out
of a four-spinor wavefunction leaving it with two degrees of freedom
(spins up and down).

We also know that to give mass to a massless vector boson, one starts
with a four-vector potential with two transverse degrees of freedom, and
adds a third longitudinal degree freedom by "swallowing" a
Nambu-Goldstone scalar. Importantly, such a mechanism is also
*predictive* of the mass.

Questions:

1) Is it proper, linguistically, to say that a Weyl spinor (R and L
projections using 1 +/ gamma^5) which solves the Dirac equation for a
zero-mass Fermion has a single degree of freedom, namely, spin up, or
spin down, because such a massless spinor, which travels at the speed of
light and can never be overtaken by a Lorentz boost, thereby yields a
precise correspondence between helicity and chirality?

2) In rough analogy to how boson mass is "revealed," would it make
sense, in principle, to consider the possibility that a *predictive*
mechanism for Fermion masses might start with two decoupled massless
Weyl spinors, one L and one R, each with one degree of freedom, and have
these two Weyl spinors "swallow" up the degrees of freedom from one
another yielding a massive
Fermion (four-component Dirac spinor) with two degrees of freedom?

Of course, one would want to ultimately show such a mechanism in detail
and arrive at the right masses. But, my question is whether this line
of inquiry makes basic theoretical sense at the outset?
Thanks,
Jay.

I'm having moderate success constructing an
electron (e-) or an (e+) using 3 charges (-) (-) (+),
or (+) (+) (-), respectively.
From that, construct a proton using (e+) (e+) (e-).
Each of those particles decay when combined
with their anti-particle. Aside from antiparticle
induced decay I think those particles are stable,
i.e. there is no evidence of spontaneous decay.

I get fair results by defining the charge above
as being a finite vector orthogonal to space &
time, which is suggestive of a 5D orthogonality,
where the 5th is finite and possess only +/-1,
sticking out of an orthogonal spacetime, along
the lines of Kaluza's 5D theories. However, I
find it's more realistic to use asymmetrical
metrics in 4D for practical applications, albiet
somewhat unconventionally.

I'll use "4" for time following classics here.

For example: Using F_14 for the electric field,
and setting in a rest frame g_14 = F_14, we
will obtain classically charge "q" by

q = E * r^2, where E = q/r^2 = Electric Field,

(Charge "q" is experimentally determined to be
quantized),

but in GR to include that we need to fracture
the metric into symmetric and asymmetric

g_uv = s_uv + a_uv,

and for brevity I'll set a_uv = q*F_uv.

Following the classical demo above,
we can do a product in the spirit of q = E*r^2,
written in terms of GR as, (A and B are charges,
A^1 and B^1 are spatial distances relativity
to charges A and B, A^4 and B^4 are the time
difference due to the differneces in spatial
location),

2AB = a_uv A^u B^v

= A*F_14 A^1 B^4 + A*F_41 A^4 B^1.

From this we can use F_14 = - F_41= E
r = A^1 = - B^1, because A and B are in relatively
opposite directions, but A^4 = B^4 =r because
the're in the same direction relatively temporally
and get,

2AB = A* E * r^2 + A*(-E) *r*(-r)

= A*E*r^2 , where E = B/r^2.

Clearly a spinor like a_uv = -a_vu was
employed to provide the relativity of
charges A and B.
By dividing by "r" the mass/energy, "m"
of a pair of charges is,

mc^2 = A*B/r , classically.

Yup, Jay's ideas make sense.
Regards
Ken S. Tucker
kst