Linked Questions

1
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0answers
56 views

Breaking of a local symmetry is impossible, so what “discrete remnant global symmetry” is the SM-Higgs breaking? [duplicate]

Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to ...
132
votes
5answers
16k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
26
votes
5answers
6k views

Noether charge of local symmetries

If our Lagrangian is invariant under a local symmetry, then, by simply restricting our local symmetry to the case in which the transformation is constant over space-time, we obtain a global symmetry, ...
34
votes
2answers
11k views

How does the Higgs mechanism work?

I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might ...
16
votes
4answers
1k views

Why does the Higgs field fall into the same ground state at all points across space?

I'm struggling to understand the concept of spontaneous symmetry breaking. I understand that the sign of the coefficient $\mu^2 > 0$ in the Higgs potential: $$ V(\phi) = \mu^2 \phi^{\dagger} \phi - ...
11
votes
2answers
2k views

Understanding Elitzur's theorem from Polyakov's simple argument?

I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
5
votes
1answer
152 views

Is the electroweak $SU(2)$ gauge symmetry an exact symmetry in Standard Model before spontaneous symmetry breaking?

In Standard model, components of a $SU(2)$ doublet (for example $u$ and $d$) have different masses. This means there is no $SU(2)$ symmetry, but I think it is okay because the $SU(2)$ symmetry is ...
10
votes
1answer
610 views

Is Elitzur's theorem valid only in lattice field theory?

Elitzur's theorem, stating that spontaneous breakdown of a gauge symmetry is impossible, was originally proved for a lattice gauge theory. Is it valid in continuum field theory? Any ref?
5
votes
1answer
456 views

Spontaneous symmetry breaking of gauge symmetry in 1+1 dimensions?

The Mermin-Wagner theorem states that continuous global symmetries cannot be broken in two or fewer spacetime dimensions; however, I have not seen this statement applied to gauge theories. Does it ...
3
votes
2answers
315 views

What is dynamical symmetry breaking, exactly?

As far as I understand, a symmetry can be broken explicitly (either by manually putting symmetry-violating terms in the Lagrangian or via an anomaly) or spontaneously. I want to focus on the second ...
1
vote
2answers
158 views

Global $U(1)$ transformation properties of gauge fields

What are the Global gauge transformations of gauge bosons in Standard Model? To elaborate: Initially, we consider the global $U(1)$ transformations of scalars ($\phi$) and fermions ($\psi$) as $$\...
2
votes
1answer
113 views

Is color charge quantized?

I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
1
vote
1answer
342 views

Gauge symmetry and symmetry breaking?

In quantum field theory we say that gauge symmetry is a redundancy, and also, in Xiao-Gang Wen's book, it reads that gauge symmetry is not a symmetry, so it can never be broken. And the Higgs ...
3
votes
1answer
75 views

Gauge transformations with varying phase give us conservation of the charge density. Hence charged particles cannot move?

I stumbled upon the following paragraph in Quark confinement and Topology of gauge theories by Polyakov "Gauge invariance with constant phase $\Psi \to e^{i \alpha}$ lead to conservation of the ...
4
votes
0answers
70 views

If the gauge symmetry is not broken by spontaneous symmetry breaking, what symmetry is broken?

In this post, the answer by buzhidao showed that the $U(1)$ gauge symmetry is not broken by spontanous symmetry broken and Higgs mechanism. What role does "spontaneously symmetry breaking" ...

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