Linked Questions

45 votes
3 answers

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 ...
an offer can't refuse's user avatar
41 votes
4 answers

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 ...
user46348's user avatar
  • 691
23 votes
6 answers

Hamiltonian for relativistic free particle is zero

One possible Lagrangian for a point particle moving in (possibly curved) spacetime is $$L = -m \sqrt{-g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu},$$ where a dot is a derivative with respect to a parameter $\...
Javier's user avatar
  • 28k
27 votes
2 answers

Invariance of Lagrangian in Noether's theorem

Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$. However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ (...
Isaac's user avatar
  • 2,880
21 votes
3 answers

Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian $$L_{1}=\partial^{\...
FraSchelle's user avatar
  • 10.4k
26 votes
2 answers

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 ...
Siva's user avatar
  • 6,048
19 votes
1 answer

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 ...
user avatar
9 votes
3 answers

Feynman's layman proof of local charge conservation And it ends at 16 minutes. I have a great love for Feynman's explanations but right now I seem to have failed to understand exactly how his example ...
AntiElephant's user avatar
14 votes
2 answers

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 ...
dolun's user avatar
  • 2,558
9 votes
2 answers

How is the term 'current' defined in QFT?

Reading papers and books about QFT, the term current is often mentioned with examples like the quark current in QCD or the electromagnetic current in QED. I was wondering, if there is a precise ...
Thomas Wening's user avatar
10 votes
2 answers

Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
alphanzo's user avatar
  • 171
2 votes
3 answers

Application of Noether Theorem

I attempt to understand one of the examples of the application of Noether theorem given in Peskin & Schroeder's An Introduction to Quantum Field Theory (Page no. 18, Student Economy Edition). The ...
rainman's user avatar
  • 2,983
6 votes
1 answer

What is the Noether charge associated with the the color $SU(3)$ symmetry of QCD?

A version of the Noether's theorem applies to local gauge symmetries. What is the Noether's charge associated with a non-abelian gauge symmetry such as the color $SU(3)$ and how is that derived? I ...
SRS's user avatar
  • 26.2k
10 votes
1 answer

In nonabelian gauge theory, does the ordinary or covariant derivative go into the statement of current conservation?

Before equation (77.35), Srednicki's QFT book says We define the chiral gauge current $j^{a\mu}$ [where $a$ is a color index]. Its covariant divergence (which should be zero, according to Noether's ...
tparker's user avatar
  • 47.2k
10 votes
1 answer

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
Prahar's user avatar
  • 25.6k

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