The Beginnings of Spontaneous Symmetry Breaking in Particle Physics

by G. S. Guralnik

I summarize the development of the ideas of Spontaneous symmetry breaking in the 1960s with an outline of the Guralnik, Hagen, Kibble (GHK) paper and include comments on the relationship of this paper to those of Brout, Englert and Higgs. I include some pictures from my "physics family album which might be of some amusement value".

http://arxiv.org/abs/1110.2253

Hello Hossein,

I have no clue about the creation of asymmetry in physical systems. However, in chemistry, asymmetry has been know as chirality since the late 1800s. Synthesizing chiral compounds has been difficult since mostly are formed in both forms. In chemistry, separation is difficult, but has been worked out. Maybe, getting the fundamentals of chirality may trigger some ideas for physics.

Cheers, Ingo

Dear Ingo

Yes, I agree with you, because the word "chiral" was derived from the Greek word for hand. Our hands are good example of chirality, they are mirror images of each other.

For space-time symmetries, we can specify the change in either of two ways: as a change in coordinates and time (equivalent to position and velocity), or as a change in coordinates and momentum.

http://oer.physics.manchester.ac.uk/AQM2/Notes/Notes-3.2.html

In any inertial reference frame and Cartesian components; in my theory there is an inseparable relationship between speed and Spontaneous symmetry breaking.

https://www.researchgate.net/publication/208380871_Zero_Point_Energy_and_the_Dirac_Equation?ev=prf_pub

Article Zero Point Energy and the Dirac Equation

Dear Hossein,

your question focuses attention on an important aspect of quantum particle interactions. In order to answer to your question I refer to my quantum gravity theory, where observed quantum interactions are encoded by means of observed quantum super Yang-Mills PDEs, say (YM)[i]. Symmetry properties of such quantum equations are not conserved, in general, by their nonlinear quantum propagators, encoding observed quantum reactions, therefore the breaking symmetry is a common phenomenon in observed quantum reactions ... However to answer to your question it is enough to think how a quantum mass-free particle (e.g. a photon) can dynamically acquire a mass-gap. This is obtained by crossing the Goldstone boundary and entering inside the sub-equation (Higgs)[i]\subset(YM)[i], where live quantum particles with mass-gap. Really from the phenomenological point of view, photons are particles considered having speed c, instead massive particles have speeds lower than c. Let me underline that my geometrodynamical formulation to justify mass acquisition is more general than the so-called Higgs symmetry breaking mechanism ! However, it can be reconduced to a symmetry breaking mechanism too, since  (Higgs)[i] is a sub-equation of (YM)[i], hence the symmetry pseudogroup group of (Higgs)[i] is necessarily lower than (YM)[i] one.

My best regards,

Agostino

Dear Agostino

"... photons are particles considered having speed c, instead massive particles have speeds lower than c."

My question is exactly the same physical reality is built that in low speed (relative to light speed) spontaneous symmetry breaking.

Please consider to speed of photon (electromagnetic interaction), and weak bosons.

Do you have any description about the relation between speed and spontaneous symmetry broken, in your theory?

Dear Hossein,

the concept of quantum particle speed is phenomenological one, since it is related to the phenomenological identification of quantum particles as point-like objects. Of course the speed of such point-like objects cannot play a fundamental role in quantum gravity. This point of view is hard to be accepted since one has considered for a century the quantum field theory founded on the special relativity kinematics ... But all that machinery has nowadays only a phenomenological relevance ! Therefore there is an indirect link between breaking symmetry and speed. With this respect, it is important to remark that the apparent-time of the observer does not correspond to the quantum-time of nonlinear quantum propagators encoding evolution of quantum particles. It is just this quantum-time that must enter in the Heisenberg's uncertainty relation. For more information see http://arxiv.org/abs/1205.2894.

In other words, according to my quantum gravity theory, your question should be changed in the following:

Does exist a direct relation between mass-gap and breaking symmetry ?

According to my previous post in this thread the answer is in the affirmative.

Regards,

Agostino 

Dears Professors Mohamed and Agostino

In generaly, there is a direct relation between the spontaneous symmetry broken and acceleration. Because " in a particle accelerator, beams of subatomic particles are boosted to nearly the speed of light..."

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=4629896

So, the question changes to " what happens for sub atomic particles in in a particle accelerator?

According to Standard Model, there is no answer about this question, because point-like concept is a stop point in this case. It means we need thought beyond the Standard Model and point-like particle.

"In 1962 Goldstone Salam and Weinberg convincingly proved that the spontaneous breaking of a continuous global symmetry in a relativistic theory requires associated zero mass excitations. This was a disappointment as they had hoped to find that there was a way around this connection. Zero mass particles in nature are simply not seen with the exception of the photon and presumably the graviton."

http://arxiv.org/abs/1110.2253

So, in addition to point-like particles, massless concept should also be reviewed.

https://www.researchgate.net/publication/208380871_Zero_Point_Energy_and_the_Dirac_Equation?ev=prf_pub

Article Zero Point Energy and the Dirac Equation

Dear Hossein!

I fear that my answer is no helpful. But a similar problem I see when examining accelerated particles.

Speed is synonymous with internal energy (=mass) of particles (resp. physical objects). This internal energy or mass leads to energetic or mass asymmetry. It is a bit similar to the basic concept of the Higgs-mechanism. Furthermore an accelerated particle could not be point-like.

I suspect that in case of superconductivity a high arranged system of electrons is disturbed by thermal movement. Fermi's electron gas is not a qarter of the true.

Best Regards

Hans

Dear Hossein,

as you just know in my quantum gravity theory, quantum particles are suitable integral chains in quantum super Yang-Mills PDEs. This of course extends the old point of view of the quantum field theory, that instead is founded on the special relativity kinematics of point-like objects. Furthermore, I proved existence of quantum particles without mass-gap. Therefore your opinion 

'..., in addition to point-like particles, massless concept should also be reviewed'

is not completely right !

My best regards,

Agostino

Dear Hans

I have understood point-like is unrealistic and barrier to better understand the /physical phenomena. Let me describe the what happens when a particle/object accelerates.

In my theory, energy is "dense field" and mass is "Intensive energy".

Bosons moves faster than light speed c, energy moves with speed of ligh (in inertial reference) and mass (particle/object) move slow that c.

So, when a particle accelerates, its elements motion change of non transmission movement to transmission.

"Fermi's electron gas is not a qarter of the true. " I have not studied it.

https://www.researchgate.net/publication/208380871_Zero_Point_Energy_and_the_Dirac_Equation?ev=prf_pub

Article Zero Point Energy and the Dirac Equation

Dear Agostino

"as you just know in my quantum gravity theory,..." Yes, I know and I learned of your theory.

Yes, you are right. In my opinion, particles have structure and massless concept is an assumption only. I have describe it in my last comment to Hans.

If we continue to believe that in the Standard Model, elementary particles are point particles and unstructured, we cannot resolve ambiguities in modern physics.

As long as you think like the past, you will get the same results that you've already earned, Feynman said.

No Hossein,

I do not believe that the Standard Model considers quantum particles point-like objects ! But SM does !

Please do not play with words when you are talking with me ... otherwise it is impossible to continue to discuss.

All the best,

Agostino

Dear Agostino

Might I do mistake, but never will do play with words. So, I With all humility ask you please correct me when I have mistake or misunderstand.

What means following paragraph?

--The Standard Model treats fundamental particles as point-like entities having no dimensions, adjusted for by a kludge called renormalization.--

I have rewrote of the last paragraph of following link.

http://www.benbest.com/science/standard.html

Best Regards

Hossein

This means that In the Standard Model quantum particles are considered as point-like objects ! But this is not my point of view ! I do not consider quantum particles point-like objects !

Agostino

Dear Agostino

Do have quantum particles structure in your theory?

Hossein

Dear Hossein,

the possible structures of quantum particles, in my quantum gravity theory, are only dynamical ones admitted from the quantum super Yang-Mills PDEs.

Agostino

Dear Hossein,

Your question, in which a spontaneous symmetry breaking is associated with a particle speed, assumes the spontaneous breaking of the Lorentz symmetry. Then the answer would be ``No", the spontaneous breaking of the Lorentz symmetry is not related to the particle velocity by definition: spontaneous violation of the Lorentz symmetry means the invariance of  the corresponding Lagrangian which, in turn, results in the invariance of the particle equation of motion which, in turn, results in the invariance of the particle Feynman propagator (which is, in the momentum space, an inverse of the Fourier transform of the equation of motion)  which, in turn, determines the maximum attainable particle speed.

On the other hand, in case of an explicit Lorentz symmetry breaking (see, e.g.,  S.Coleman and S. Glashow (Phys. Rev. D59, 116008-1-116008-14, 1999 ``High energy tests of Lorentz invariance)   the maximal attainable speeds are different for different kinds of particles.

Dear Vassili

"... the maximal attainable speeds are different for different kinds of particles."

Exatly, it deppends to structure of particles.

In pair production, a photon that moves with speed c, converts to electron and positron that move with speed v