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. ...

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Double $U(1)$ local gauge invariance derivative

In QED and the basic Higgs mechanism, there is a local gauge transformation where a scalar field $\phi$ is transformed as: $e^{i\theta\eta(x)} \phi$ The partial derivative of this however makes the ...
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1answer
23 views

Electric Magnetic potential and Lorentz transform [on hold]

I have heard that the scalar potential and the magnetic vector potential in the electromagnetic four potential become the four vector by the Lorentz transform. Thereafter, the Lorentz transform leads ...
2
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1answer
32 views

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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0answers
14 views

dual variables for lattice fermions

I am quite familiar with duality transformations for lattice spin systems (i.e. systems with global $O(n)$ symmetry) and pure gauge systems (i.e. local $SU(n)$). However, after searching for a bit, I ...
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1answer
22 views

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 ...
7
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1answer
69 views

Connection beween infinite gauge symmetries and UV finiteness

In e.g., http://arxiv.org/abs/arXiv:0712.3526 the author claims: Since the massless higher-spin field theories involve infinite-dimensional gauge symmetries, one expects that such theories may be ...
6
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1answer
77 views

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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0answers
37 views

General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
4
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1answer
107 views

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 ...
8
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1answer
184 views

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 ...
6
votes
2answers
135 views

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 ...
3
votes
1answer
87 views

What are type system examples of local gauge transformation- and field strength-like objects?

This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types. A field $$\psi:\mathcal M\to\mathbb C^n$$ is a section of the ...
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vote
1answer
74 views

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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1answer
48 views

Gauge field with flat connection

Consider a gauge field $A_z^a$ with a flat connection $$F_{z{\bar z}}^a = \partial_z A_{\bar z} ^a - \partial_{\bar z} A_z^a + f_{bc}{}^a A_z^b A_{\bar z}^c = 0$$ where $f_{bc}{}^a$ is the structure ...
4
votes
2answers
109 views

How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have?

The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are ...
2
votes
1answer
87 views

Why do we require the generators of $\mathrm{SU(N)}$ gauge theories to be $N \times N$ matrices?

I have often read that the generators for $\mathrm{SU(N)}$ gauge theories must be $N \times N$ matrices; see for instance these notes at the top of page 3: ...
10
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1answer
169 views

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 ...
11
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3answers
620 views

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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votes
1answer
92 views

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 ...
4
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0answers
67 views

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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0answers
48 views

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 ...
2
votes
1answer
74 views

Adding stuff to the path integral (Faddeev-Popov method)

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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1answer
55 views

How to obtain Maxwell's Lagrangian from complex scalar fields?

I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to ...
3
votes
3answers
236 views

Multivariable Dirac Delta and Faddeev-Popov Determinant

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 ...
3
votes
1answer
78 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 \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. ...
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votes
1answer
60 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?
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1answer
122 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 ?
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0answers
91 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 - ...
8
votes
1answer
162 views

Sign in the photon propagator

The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...), \begin{equation} \frac{ i }{ p ^2 - m ^2 + i \epsilon } \end{equation} The photon propagator ...
5
votes
1answer
139 views

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 ...
7
votes
1answer
183 views

What is the conclusion from Aharonov-Bohm Effect?

What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
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0answers
47 views

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 ...
2
votes
0answers
125 views

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 ...
3
votes
0answers
52 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
70 views

Field strength vanishes iff $A_{\mu}$ is pure gauge

Is it true that the field strength $F_{\mu\nu}$ in a non-abelian YangMills case with gauge group $G$ vanishes is and only if the gauge field $A_{\mu}$ is a pure gauge? I can show one implication. ...
2
votes
0answers
44 views

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 ...
3
votes
0answers
73 views

Why is general relativity considered to be a gauge theory? [duplicate]

I have studied the first five chapters of Carroll's book (up to the Schwarzschild solution). I see similarities to the Yang-Mill theories such as the covariant derivative to account for curvature in ...
3
votes
0answers
33 views

Quiver and Gauge theory

i want to know how to construct a quiver of a Gauge theory specified by groupe g with rank=r ?
2
votes
1answer
37 views

Non-vanishing commutator of potential and mass matrices for Majorana fermions interaction theory

Consider 2 different Majorana fermions $\Psi_{L}, \Psi_{R}$ (physically, neutrinos). In general case I can write the massive part of lagrangian of these fermions in the form $$ L_{m} = (\bar ...
8
votes
1answer
92 views

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 ...
2
votes
0answers
32 views

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 ...
3
votes
0answers
64 views

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 ...
1
vote
1answer
83 views

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 \begin{equation} e^{-i a_i \sigma_i} \gamma_\mu e^{i a_i \sigma_i} = \gamma_\mu ...
5
votes
1answer
132 views

Is the gauge fixing $\partial_\mu A^\mu + \gamma A_\mu A^\mu=0$ used in the literature and does it have a name?

In an exercise for a course on Gauge Theories, I was asked to derive the action of QED with the method by Faddeev and Popov, using the following gauge-fixing function: $$F(A) = \partial_\mu A^\mu + ...
6
votes
1answer
176 views

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 ...
1
vote
3answers
285 views

Difference between $SU(2)$ and $SU(2)$ gauge transformations?

I hear this jargon all the time, so what is the difference? (Of course this is nothing special to $SU(2)$, but rather I just took it as an example)
3
votes
2answers
413 views

Gauge Invariance of the Hamiltonian of the electromagnetic field

The Hamiltonian for an electron of mass $m$ and charge $e$ in an exterior electromagnetic field is $$H=\frac{1}{2m}(p-(e/c)A)^2+e\varphi.$$ The corresponding (via canonical quantization) quantum ...
3
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0answers
122 views

Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & ...
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0answers
53 views

Doubt on Kaluza-Klein theories by Bailin/Love

I've started reading a review written by D. Bailin and A. Love about Kaluza/Klein theories: Bailin, D., & Love, A. (1987). Kaluza-Klein theories. Rep. Progr. Phys., 50(9), 1087. ...
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vote
0answers
45 views

Dual photon in d=3

In some papers (such as http://arxiv.org/abs/hep-th/9910184 and http://arxiv.org/find/all/1/all:+AND+kapustin+AND+topological+disorder/0/1/0/all/0/1) I am reading it is always referred at "the dual ...