# Tagged Questions

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### Global vs. local gauge group in mathematical sense - physics examples?

Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group: Local gauge group $G$. Corresponds to the fibers of the ...
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### History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, but could you explain the history? It's ...
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### Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
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### Why gauge $SU(N)$ and not $SO(N)$?

When building models people typically gauge $SU(N)$ but rarely try to gauge $SO(N)$ (the only example I know about is $SO(10)$, but even that isn't quite $SO(10)$ but actually its double cover). At ...
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### A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
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### Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies Gauge redundancy for 1-forms,'photons'. Does this argument go through to p-forms? That is does lorentz invariance of s-matrix of ...
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### Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
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### Equations of motion for the Yang-Mills $SU(2)$ theory

I have an exercise for Yang-Mills theory. I can't find answer anywhere. Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar ...
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### A graphical proof that the $SU(2)/\mathbb{Z}_2$ vortex is non-orientable

The text, see [1], compares the vortex solutions of a spontaneously broken symmetry $U(1) \rightarrow 1$ and $SU(2)\rightarrow U(1) \rightarrow \mathbb{Z}_2$. The vortices can be classified by ...
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### A question about propagator of Maxwell field in different gauge

The propagator of Maxwell theory is different, depending on the gauge fixing procedure used. Then why will the S-matrix elements be the same for the same process in different gauges?
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### Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action?

In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must ...
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### Anomalous Dimensions of Gauge Interactions

Peskin and Schroeder mention a few times that the anomalous dimension of a gauge interaction operator is zero. The justification for this is that the charge operator shouldn't get modified under ...
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### The BRST construction for YM with or without auxiliary field

I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as ...
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### The gauge covariant derivative and it's substitution

I was wondering wether it would make a difference (in general) if I were to were introduce the gauge covariant derivative $$D_\mu=\partial_\mu+ieA_\mu$$ In the Lagrangian density and then derive the ...
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### Question on derivation of Ward identity

I'm currently reading these notes about the Ward identity (pages 259 - 261). I will repeat some of the steps to make the question self-contained. Let us consider a local transformation on the field ...
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### 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 ...
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### Why am I wrong about how to view gauge theory?

Edit: I know there have been some similar questions but I don't think any had quite articulated my particular confusion. If gauge symmetries are really just redundancies in our description accounting ...
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### Integrating the gauge covariant derivative by parts

I was watching a set of lectures on effective field theory and the lecturer said that you can always integrate the covariant derivative by parts due to gauge symmetry. For example, if I understand ...
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### Unitary gauge for non-abelian case

I'm reading Chapter 19 of Mandle and Shaw's Quantum field theory. In the first section it is explained that one can go with a $SU(2)$ followed by a $U(1)$ transformation from ...
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### Inverse of gauge covariant derivative

Consider the gauge covariant derivative defined by $$D_z = d_z + \Delta_z$$ or explicitly $$(D_z)^a{}_c = \delta^a_c d_z + (\Delta_z)^a{}_c = \delta^a_c d_z + f_{bc}{}^a A_z^b$$ Here, $d_z$ is the ...
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I'm wondering about the Faddeev-Popov method described in Peskin Schroeder and also on page 7 in this link. What gives them the right to simply add the Gaussian $\omega$ and thus introduce the $\xi$ ...
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From this mathstack page and in particular Qmechanic's answer: There exists an $n$-dimensional generalization $$\tag{1} \delta^n({\bf f}({\bf x})) ~=~\sum_{{\bf x}_{(0)}}^{{\bf f}({\bf ... 1answer 93 views ### What is the constraint on the Gauge Potential in the Covariant Gauges? One of the most common gauges in QED computations are the R_{\xi} gauges obtained by adding a term $$-\frac{(\partial_\mu A^{\mu})^2}{2\xi}$$ to the Lagrangian. ... 1answer 92 views ### Gauge fixing of an arbitrary field How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing? 1answer 172 views ### Gauge fermions versus gauge bosons Why are all the interactions particle of a gauge theory bosons. Are fermionic gauge boson field somehow forbidden by the theory ? 0answers 147 views ### Non abelian gauge theory with charged scalar field Suppose we have an SU(N) non abelian gauge theory coupled with a multiplet of complex scalar fields \Phi. The lagrangian would be$$ L= - \frac 12 \text{Tr } F_{\mu\nu}F^{\mu\nu} + |D_\mu \Phi|^2 - ...
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The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...), $$\frac{ i }{ p ^2 - m ^2 + i \epsilon }$$ The photon propagator ...
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### About the gauge formalism in statistical quantum field theory

I would like to understand a bit more the aspects of the gauge theory in statistical field theory. In particular, I would like to understand how the replacement $\tau \rightarrow it/\hbar$ is ...
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### Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
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### what is 't Hooft up to? [closed]

apart of the 't Hooft diagrams that you all love (and find all sort of dualities starting with them) one of the venues 't Hooft works nowadays is apparently some sort of "deterministic representation ...
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### A question about the constraints in BRST-Fock theories

In BRST Symmetry in the Classical and Quantum Theories of Gauge Systems, Henneaux says the Fock representation is not applicable to an odd number of constraints. Then he goes on to say that the ...
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### Complex Representation of a gauge group and a Chiral Gauge Theory

In this John Preskill et al paper, a statement is made in page 1: We will refer to a gauge theory with fermions transforming as a complex representation of the gauge group as a chiral gauge ...
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### Twisted supermultiplets

What is a twisted supermultiplet, in a generic supersymmetric theory? Which ordinary fields belong to one of such twisted supermultiplets? I am confident with the idea of a supermultiplet or a ...
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### Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
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### Global SU(2) invariance of QED Lagrangian

I'm having problems seeing the global SU(2) invariance of the QED Lagrangian. My specific problem is seeing why e^{-i a_i \sigma_i} \gamma_\mu e^{i a_i \sigma_i} = \gamma_\mu ...