1
vote
1answer
41 views

Is internal symmetry the same as gauge symmetry?

This is more a terminology question. I have seen that some people differentiate between the two types of symmetry: internal symmetry and gauge symmetry (of a field theory). Is there a difference (in ...
3
votes
1answer
207 views

Which transformations *aren't* symmetries of a Lagrangian?

As far as I understand, Noether's theorem for fields works, as explained in David Tong's QFT lecture notes (page 14) for example, by saying that a transformation $\phi(x) \mapsto \phi(x) + \delta \phi ...
0
votes
1answer
38 views

Conserved current for a constant translation of a free massless scalar field

In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field: $$S(\varphi) = \frac{1}{2}\int ...
4
votes
1answer
114 views

Conceptual question about field transformation

(c.f Conformal Field Theory by Di Francesco et al, p39) From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not ...
3
votes
1answer
96 views

Translations and Noether's Theorem

I'm fine with $U(1)$ symmetry and Noether's Theorem, but struggling with the translations of the field; namely $$\phi'(x^{\mu})=\phi(x^{\mu}-a^{\mu}),$$ where $a^{\mu}$ constant four-vector ...
6
votes
1answer
167 views

Symmetries in physics

Can you explain me some of the mathematical details of such concept as symmetries? In physics, we have some manifold, and fields are functions on this manifold. On the one hand, we have symmetries of ...
7
votes
1answer
220 views

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 ...
3
votes
0answers
78 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
2
votes
1answer
123 views

Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
8
votes
1answer
192 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills ...
1
vote
0answers
57 views

Global part of a local symmetry?

What is exactly meant by "Global part of a Local symmetry"? What are its implications on a field theory at classical level? What are its implications at quantum level? How is it related to symmetry ...
2
votes
2answers
219 views

Does a constant factor matter in the definition of the Noether current?

This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is: Consider a field Lagrangian with only ...
3
votes
1answer
722 views

Local and Global Symmetries

Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory? Heuristically I know that global ...
6
votes
1answer
462 views

U(1) Charged Fields

I don't quite understand what is actually meant by a field charged under a $U(1)$ symmetry. Does it mean that when a transformation is applied the field transforms with an additional phase? More ...
2
votes
1answer
293 views

How to perform a scale (invariance) transformation?

According to this wikipedia article in the $\phi^4$ section, the equation $$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$ in 4 dimensions is invariant ...
1
vote
1answer
338 views

Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity

I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
18
votes
1answer
552 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 ...