Questions tagged [gauge-symmetry]
45 questions
44
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 the conserved current here…
user46348
- 721
28
votes
2 answers
Are there massless bosons at scales above electroweak scale?
Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for Higgs mechanism, gauge bosons $Z$ & $W$ have masses about 100 GeV. But before this spontaneous symmetry breaking ( i.e. Energy > 100…
Eleuname
- 383
27
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 symmetry: to my understanding, it's a redundancy in…
Siva
- 6,204
20
votes
1 answer
What is a "free" non-Abelian Yang-Mill's theory?
I hope this question will not be closed down as something completely trivial!
I did not think about this question till in recent past I came across papers which seemed to write down pretty much simple looking solutions to "free" Yang-Mill's theory…
Student
- 4,611
19
votes
3 answers
What is the basis of gauge theory?
I’m learning about gauge concepts. I’ve always had the idea that by looking at a phenomenon from different viewpoints, that symmetries could be derived – in fact, that was what an equal sign signified. In other words, the underlying phenomenon…
Beaglet
- 313
- 4
- 6
18
votes
1 answer
Why mass terms are forbidden?
I would like to clarify my understanding on why mass terms in Lagrangians of gauge theories are forbidden.
It's often repeated that particle masses are forbidden by electroweak symmetry because it is a chiral theory. I want to make a distinction…
David Hall
- 283
18
votes
1 answer
Gauge fixing and degrees of freedom
Today, my friend (@Will) posed a very intriguing question -
Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions related by a gauge transformation are identified…
Prahar
- 29,157
17
votes
3 answers
Coulomb gauge fixing and "normalizability"
The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as
$$
A_\mu\to A_\mu'=A_\mu+\partial_\mu\theta
$$
for some…
joshphysics
- 58,991
15
votes
1 answer
Do gauge bosons really transform according to the adjoint representation of the gauge group?
Its commonly said that gauge bosons transform according to the adjoint representation of the corresponding gauge group. For example, for $SU(2)$ the gauge bosons live in the adjoint $3$ dimensional representation and the gluons in the $8$…
jak
- 10,431
14
votes
1 answer
Gauge invariant but not gauge covariant regularization
I'm not sure if someone's already asked this before, but I was wondering, in field theory,
when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In particular, in Wikipedia, the regulator of…
Joman
- 193
14
votes
2 answers
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 gauge-invariant quantities can have finite…
VanillaSpinIce
- 1,458
13
votes
1 answer
Gauge Invariance of the Non-abelian Chern-Simons Term
I'm trying to prove that, under the gauge transformation $$A_{\mu} \rightarrow A_{\mu}^{\prime} = g^{-1} A_{\mu} g + g^{-1} \partial_{\mu} g,$$ the non-abelian Chern-Simons Lagrangian density:
$$\mathcal{L}_{CS} = \kappa \epsilon^{\mu \nu \rho} tr…
Gary B
- 139
11
votes
2 answers
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 both local and global case), and if there is what…
Hamed
- 405
- 2
- 10
9
votes
1 answer
Some questions about Ward-Takahashi Identity
I'm a learner of Peskin and Schroeder's textbook of quantum field theory.
I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference.
The following is the Ward-Takahashi identity, where $M^{\mu}$ is…
Brioschi
- 1,055
8
votes
1 answer
Is reparameterization invariance some kind of gauge symmetry?
On page 116 of this book it is said, that reparameterization invariance of the string action is analogous to the gauge invariance in electrodynamices.
Whereas Maxwell's equations are symmetric under a gauge transformation which allows to describe…
Dilaton
- 9,771