Talk:Higgs mechanism

Can we solve the problem of Higgs mechanism by proving the hypothesized Higgs boson does not exist at all?

Yes, we can. The brief answer is in http://mechanism-revealedphysics-bcz37.blogspot.com/

BCZ§ —Preceding unsigned comment added by BingchengZMRP (talk • contribs) 18:40, 23 March 2010 (UTC)

Mathematical parts

The sections with equations in them have the following structure--- first explain the nonrelativistic case of the Landau model of superconductivity, a charged nonrelativistic field with a vacuum expectation value, then explain the relativistic case, which is a charged scalar field with a vacuum expectation value (the only difference is the relativistic invariance of the condensate--- the calculations are exactly the same), finally do the full-blown nonabelian Higgs mechanism. This is the structure of the article, and recent edits have made it unreadable.

This is more or less the historical order of development, the Landau model of 1961 and the Stueckelberg analysis of 1957 is followed by the Brount-Englert 1964 paper. There is nothing controversial here, and anyone who is confused about the accuracy of any of the statements here is too ignorant to work on this article.69.86.66.128 (talk) 05:22, 27 August 2010 (UTC)

Local symmetries CANNOT be spontaneously broken

I think there are two problems with this article

1) It is a common misconception among students and even young researchers that SSB of local symmetries is possible, this primarily originates from simplified (and sometimes wrong) explanations of the Higgs mechanism in introductory QFT books (Peskin & Schroeder, and many other similar books). As the famous Elitzur theorem says, spontaneously breaking of local symmetries is impossible! See >>Phys. Rev. D 12, 3978–3982 (1975)<<. What is really happening is that the local symmetry is EXPLICITLY broken by a gauge fixing procedure and THEN it is possible to break the remaining GLOBAL symmetry.

This is also mentioned on scholarpedia (Kibble, one of the fathers of the mechanism, is the Curator): >>This mechanism is often said to exhibit "spontaneously broken gauge symmetry". That is a convenient shorthand description, but the terminology is potentially somewhat misleading. The process of quantization requires a choice of gauge, i.e., an explicit breaking of the gauge symmetry. However, the resulting theory does retain a global phase symmetry that is broken spontaneously by the choice of the phase of $\langle \phi \rangle$.<<

2) The introduction indicates that the Higgs mechanism is only connected to particle physics, this is of course not true. It is widely known that the mechanism originates from superconductivity (and first noticed by Anderson), but it is today used in many different Condensed Matter systems (Condensed Matter physicists call it the Anderson-Higgs mechanism). My point is that the mechanism is also widely used in modern theoretical Condensed Matter physics (also in non-superconductors) and the article should also equally discuss this aspect.

A last comment. In this comment section, the user Bakken has written tons of inaccurate, misleading and even wrong statements. Let me correct one of these: Bakken repeatedly claim that there is no fundamental/microscopic theory of superconductivity. This is utterly wrong, for conventional superconductors a very successful theory has been known since 1957 (BCS-theory) and was awarded the noble prize in 1972. For high Tc-superconductors a microscopic theory is not fully developed (although the ingredients are well known), but this is irrelevant wrt. Higgs mechanism.

Element4element4 (talk) 22:16, 21 September 2010 (UTC)

Dear Elemnet4element4, thank you for reading my statements, I am truly flattered :). Although it is not quite clear to me what exactly your point is, but please note that the term spontaneous symmetry breaking refers to the symmetry of the ground state of the system, not the symmetry of the Lagrangian. It can happen, that the Lagrangian of a system has certain symmetry, but its ground state has not. That's precisely what the term "spontaneous symmetry breaking" signifies: the Lagrangian is symmetric, but the ground state is not. Again: it is not the symmetry of the Lagrangian that is broken (you are right here -- it can not be broken), it is the symmetry of the ground state that is broken. Note also that *that* article of Higgs is called "Broken Symmetries and the Masses of Gauge Bosons" :) Bakken (talk) 23:04, 22 September 2010 (UTC)

About the theory of superconductivity: BCS is not an a-priori microscopic solution of quantum-mechanical many-electron problem in a metal. BCS is only a crude phenomenological approximation to this complicated solution. For example, BCS can not predict from the first principles the critical temperature for any real metal. BCS is simply a generic effect in mean-field models of fermionic systems (understood with the Bogoliubov transformation). I personally do not call a mean-field model "a fundamental theory" ;) A Nobel prize for a theory does not necessarily mean that the theory is fundamental. For example, Lev Landau received a Nobel prize for a phenomenological theory of super-fluidity. Bakken (talk) 23:04, 22 September 2010 (UTC)

charged particles

In classical physics, all charged particles have mass as a result of the electromagnetic field surrounding them. (Granted, you have to add general relativity in order to keep that mass finite!) Does this not happen in quantum field theory? Harryjohnston (talk) 04:10, 18 May 2011 (UTC)

Yes, it does. Look up mass renormalization. Dauto (talk) 00:43, 19 May 2011 (UTC)

OK, so why do the W particles need the Higgs mechanism to have mass? (The same question may apply to, e.g., the electron, except that there seem to be conflicting opinions about whether the Higgs mechanism is responsible for fermion mass or not.) Harryjohnston (talk) 01:50, 23 May 2011 (UTC)

In quantum field theory a particle's mass is generated by a specific term in the Lagrangian. The W is a gauge boson which means the Lagrangian has a symmetry called gauge symmetry. It so happens that the mass term for a vector boson does not obey the gauge symmetry so by force a gauge boson must be massless unless the gauge symmetry is broken somehow. The Higgs mechanism provides a method for the gauge symmetry to be (dynamically) broken allowing for a mass term for the Z, the two Ws but not for the photon since the higgs particle does not interact with the photon which therefore remains massless. Dauto (talk) 04:39, 23 May 2011 (UTC)

Sorry, I'm still missing something. The mass that a particle acquires by virtue of being charged is surely due to the term in the Lagrangian describing the interaction between the charge and the electromagnetic field. If this term doesn't have gauge symmetry, how can a gauge boson be charged in the first place? Or does that mean that the Higgs mechanism is necessary to allow the W particles to be charged? Harryjohnston (talk) 20:35, 23 May 2011 (UTC)

At high energies the Lagrangian has a symmetry described by the symmetry group $U(1)_{Y}\times SU(2)_{L}\times SU(3)_{C}$. The first factor is the weak hypercharge gauge symmetry group, the second factor is the weak isospin gauge symmetry group, and the last factor is the strong force gauge symmetry group which is not important for what I'm about to explain. Don't confuse those groups with the flavor isospin and flavor hypercharge which are not gauge groups. The latter are mere accidental symmetries with no dynamics in themselves. Note the absence of the electromagnetic symmetry group. At lower energies through the Higgs mechanism this symmetry is reduced to the smaller group $U(1)_{em}\times SU(3)_{C}$ where both weak isospin and weak hypercharge symmetries have been broken being replaced by the electromagnetic gauge symmetry group as a residual symmetry. Clearly electromagnetism is not independent from hypercharge and isospin which is shown by the Gell-Mann–Nishijima formula: $Q=I_{3}+{\frac {1}{2}}Y.\$, where Q is the charge, I3 is the third component of the isospin and Y is the hypercharge. The point is that eventhough the W+, W-, and Z particles have different charges, seemly violating the isospin symmetry, they all in fact have the same hypercharge but have different values for the third component of their isospin, as would be expected from members of a isospin triplet. Dauto (talk) 16:37, 24 May 2011 (UTC)

Thanks. I think with a bit more thought I'll almost understand that, though I'll probably need to brush up on isospin first. At any rate now I at least know that there definitely is an answer. :-) Harryjohnston (talk) 23:22, 24 May 2011 (UTC)

Lay explanation

Would it be possible to give the gist of the mechanism for the informed lay person? For instance, I know something about physics, but I'm not a physicist; I understand the gist of spontaneous symmetry breaking, quantum probability amplitudes, spacetime curvature etc. But I can't make any sense of this article. --Doradus (talk) 15:15, 27 July 2011 (UTC)

Yes, it would, but physicists are notorious for their failure to communicate through the common language. This points out the actual problem with this article. The article is composed of a series of sentences whose interconnection is disjoint. Literally, each sentence could be written as a stand alone paragraph. A physics article can get technical but only by building upon simpler, if brief, previously stated sentences in topical paragraphs. It isn't necessary to cover the entire field of physics by leaning on principles or words which could be mentioned and highlighted as referential links. For example,

Abelian Higgs Mechanism

"Gauge invariance means that certain transformations of the gauge field do not change the energy at all".

Gauge invariance hasn't been defined nor has it been linked to a definition. The above pseudo definition is vague or misleading. It says, "transformations (do not) change". If you're experienced with these concepts, what is omitted is understood. In wiki we seek to provide explanations that are complete up to concise. That only can be achieved by hyperlink to stay within rigor and brevity, but if a reader has the patience to link out for substance, then the most abstruse concepts can be reified in a short section.

The next sentence which should be a separate paragraph even though it attempts to qualify the pseudo definition is also unclear.

"If an arbitrary gradient is added to A, the energy of the field is exactly the same".

What is "A"? Gradient of what? A physicist knows that it's the EM vector potential, so that if A is replaced by A + d(potential) the resulting equation has the same form (invariance), but the intelligent lay reader may not know.

However, the above may be relegated to mere nitpicks against the below:

"This makes it difficult to add a mass term,"

Add a mass term? What? Weren't we talking about ethereal gauge fields and their invariance? For that matter gauge field hadn't been defined nor linked either. Why do I want to add a mass term? What is a mass term? Indeed, this whole program of seeking to add mass in some electromagnetic form may be specious! Staying within the standard model we would like to present the vogue prevailing view, but we must do so with foundation. Doing so is critical for clarity about the purpose that Higgs, et al, had in creating a mechanism to explain why certain particles which act like massless quantum fields(link required) can suddenly have mass(no link on "mass" because of the ambiguity lurking in the vogue prevailing view).

It gets worse:

"because a mass term tends to push the field toward the value zero".

Push? And, what is a "value zero"? A "value, zero". Different objects. The naive reader may not understand the elision!

Coup de grace:

"But the zero value of the vector potential is not a gauge invariant idea".

Is this the origin of mass? A trick played by nature? Or, is it merely a poorly worded sentence?

"What is zero in one gauge is nonzero in another".

How is this sentence connected with the previous sentence? That has to be explicated.

The article then opens the next paragraph with,

"So in order to give mass to a gauge theory, the gauge invariance must be broken by a condensate".

The word, "condensate" is ambiguous unless the entire article is understood to be referring to the Higgs model form as applied to solid state physics, or that "condensate" refers abstrusely to a vacuum, a ground state, otherwise. These are profoundly different arenas, or are they? Is matter prior to vacuum or vice versa or are these notions categorically disjoint? These are issues of foundations which hardly can be touched in a survey. In any case this article should reside in a section dedicated to solid state physics while a companion form would reside in foundations of the standard model.