Linked Questions

113
votes
9answers
30k views

What, in simplest terms, is gauge invariance?

I am a mathematics student with a hobby interest in physics. This means that I've taken graduate courses in quantum dynamics and general relativity without the bulk of undergraduate physics courses ...
37
votes
3answers
6k views

What role does "spontaneously symmetry breaking" played in the "Higgs Mechanism"?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
37
votes
3answers
8k views

Noether's theorem and gauge symmetry

I'm confused about Noether's theorem applied to gauge symmetry. Say we have $$\mathcal L=-\frac14F_{ab}F^{ab}.$$ Then it's invariant under $A_a\rightarrow A_a+\partial_a\Lambda.$ But can I say that ...
24
votes
2answers
2k views

Why do we seek to preserve gauge symmetries after quantization?

Gauge symmetries do not give rise to conservation laws via Noether's theorem, and they represent redundancies in our description of the system. So why do we want to keep them after quantization? For ...
26
votes
2answers
6k views

Physical difference between gauge symmetries and global symmetries

There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
14
votes
2answers
3k 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 ...
11
votes
4answers
3k views

What is spontaneous symmetry breaking in QUANTUM GAUGE systems?

Wen's question What is spontaneous symmetry breaking in QUANTUM systems? is cute, but here's an even cuter question. What is spontaneous symmetry breaking in QUANTUM GAUGE systems? There are some ...
12
votes
3answers
1k views

Can we do path integrals in gauge theories without fixing a gauge?

I am aware that when quantizing gauge theories with a path integral, one needs to add a gauge fixing term to avoid over-counting gauge related field configurations. From an aesthetic perspective, I ...
16
votes
1answer
6k views

Noether's first theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's first theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
22
votes
1answer
2k views

Why does charge conservation due to gauge symmetry only hold on-shell?

While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
12
votes
1answer
3k views

What is the relationship between string net theory and string / M-theory?

I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
13
votes
2answers
2k views

Classical EM : clear link between gauge symmetry and charge conservation

In the case of classical field theory, Noether's theorem ensures that for a given action $$S=\int \mathrm{d}^dx\,\mathcal{L}(\phi_\mu,\partial_\nu\phi_\mu,x^i)$$ that stays invariant under the ...
21
votes
1answer
1k views

Phase Structure of (Quantum) Gauge Theory

Question: How to classify/characterize the phase structure of (quantum) gauge theory? Gauge Theory (say with a gauge group $G_g$) is a powerful quantum field theoretic(QFT) tool to describe many-body ...
6
votes
2answers
3k views

Where does the mass term come from in the Proca Lagrangian?

There are many good books describing how to construct the Lagrangian for an electromagnetic field in a medium. $$ \mathcal{L}~=~-\frac{1}{16\pi}F^{\mu\nu}F_{\mu\nu}-\frac{1}{c}j^{\nu}A_{\nu} $$ ...
5
votes
3answers
1k views

Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...

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