# Questions tagged [gauge-theory]

A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

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### How large is large $N$?

I once heard Lenny Susskind relate the question: "how many particles do you need in a box for the ideal gas law to 'pretty much' hold?" Obviously this question requires a notion of 'pretty ...
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### Wilson action equations of motion

Let $S_W$ be a Wilson action of $1\times 1$ plaquettes for a gauge group $G$: \begin{equation*} S_W = \beta a^4 \sum_P \left( 1-\frac{1}{N_G} \text{Re Tr}(U_P) \right), \end{equation*} where $\beta$ ...
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### Trace properties of the gauge potential in non-Abelian gauge theory

I want to proof equation 69.18 in Srednicki's book "Quantum field theory", which reads: \begin{equation} A_\mu^a(x)=2\text{Tr}[A_\mu(x)T^a].\tag{69.18} \end{equation} $A_\mu(x)$ is the non-...
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### Equation of motion of the curvature form $F$ in Yang-Mills theory

Following 4.2.1 in this document (Muharrem Küskü, The Free Maxwell Field in Curved Spacetime, 2001), I tried to adapt the method used (in particular equations 4.21 and 4.32) to Yang-Mills theory ...
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### Mathematical Charges in Classical Physics, General Relativity and QFT

I have a very easy, and naive, question: given a field $\mathbf{A}$ on some vector space $V$, we can calculate how the flux or circulation of this field behaves. For example, we have Gauss's laws for ...
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### Difference between field-antifield and light-cone quantisation

I have learnt field-antifield quantisation and know that it can be used for very general gauge theories - open and reducible. I have not got much into light-cone quantisation but I am unable to see ...
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### Higher form symmetries and Yang Mills

I have been reading about higher-form symmetries, particularly how they are applied to non-abelian gauge theories. I have come across the claim that pure $SU(N)$ Yang Mills (i.e. with no quarks) ...
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### How local gauge invariance explain charge conservation and electromagnetic force appearance?

Without electromagnetic coupling, the QM charged particle wave function is not invariant under a local gauge transformation — one with a phase that depends on space (space-time): \begin{equation} \psi ...
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### When we use Lorenz gauge or Coulomb gauge, the result formula for electric $E$ and magnetic field $B$ is same or different?

Gauge condition can be chosen as you like or not? is the Lorenz gauge is the only one correct? If Coulomb gauge can obtained exactly same results as Lorenz gauge for the electromagnetic fields E and ...
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### Can a gauge transformation eliminate singularity of gauge potential?

Suppose I have a gauge potential $A$ which goes to infinity at some point $x_0$. Can I use a gauge transformation \begin{equation} A'=U^{-1}AU+U^{-1}dU,~~~U=\exp\{-i\alpha^a(x)T^a\} \end{equation} to ...
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### Gauging R-Symmetry

I know that if one gauges the supersymmetry group, you get supergravity. You can then further gauge the R-symmetry and these are the so-called gauged supergravities. But I don't think I've seen anyone ...
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### What books would you recommend to understand mathematically the Dirac matter

I am a math student who got interested in the topics above also i want to learn about the Dirac matter the spinors the Einsteins GR and the Yang-Mills Maxwell Anderson Higgs theories and models and ...
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### Deriving a general gauge-invariant photon propagator

My understanding is that for a $U(1)$ gauge field $A_\mu$, the most general gauge-invariant kinetic term in the Lagrangian that can be written down which satisfies gauge invariance is something of the ...
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### Positive Definiteness of Killing Form in Gauge Theory

This question is related to requirement that the gauge group of a gauge theory be a direct product of compact simple groups and $U(1)$ factors but is not the same as, for example, this question (...