Linked Questions

0 votes
0 answers
33 views

Physical significance of Gauge transformations [duplicate]

Ok so a Gauge invariance is an invariance under a gauge transformation, a gauge transformation for a field is usually of the form: $\Phi\rightarrow\Phi + \frac{\partial S}{\partial\lambda}$. According ...
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118 votes
9 answers
33k 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 ...
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42 votes
3 answers
7k views

What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneous symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
39 votes
3 answers
10k 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 ...
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30 votes
2 answers
7k 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 ...
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25 votes
2 answers
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 ...
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15 votes
2 answers
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
4 answers
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 ...
13 votes
3 answers
2k 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 ...
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19 votes
1 answer
7k 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 ...
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24 votes
1 answer
3k 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 ...
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13 votes
2 answers
3k 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 ...
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13 votes
1 answer
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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 ...
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21 votes
1 answer
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 ...
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6 votes
2 answers
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. $$ \mathcal{L}~=~-\frac{1}{16\pi}F^{\mu\nu}F_{\mu\nu}-\frac{1}{c}j^{\nu}A_{\nu} $$ ...

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