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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5
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2answers
137 views

Akin to gauge field, why GR's lagrangian is not $R_{abcd}R^{abcd}$? What's the mathematical or physical meaning of $R_{abcd}R^{abcd}$?

For gauge field theory, the Lagrangian of the gauge field is $$\mathcal{L}=-\frac{1}{4}\mathrm{tr}(\mathcal{F}_{\mu\nu}\mathcal{F}^{\mu\nu})=-\frac{1}{8}F_{a\ \mu\nu}F^{a \ \mu\nu}$$ The field ...
1
vote
0answers
31 views

The Quantum Double of a Group and its relation to discrete gauge theories

Why is it that the algebraic structure known as the Quantum Double $D(G)$ of a discrete group is said to classify the excitations of a Discrete Gauge Theory (minimally coupled with matter) with gauge ...
2
votes
3answers
116 views

About constraints of the first class and electrodynamics

Let's have some theory in hamilton formalism and let's assume that it has the constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx ...
2
votes
1answer
92 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 ...
0
votes
0answers
26 views

Understanding better this physical phrase [duplicate]

In field theory, symmetry governs the dynamics by restricting the form of the Lagrangian from which all relevant equations and interactions are derived. An example of symmetry transformations is ...
0
votes
1answer
41 views

Can the physical properties of the EM field be described directly from the 4-gauge potential?

I'm trying to make an argument that classically, the EM field is considered a more 'real' physical quantity than the potentials, and am tempted to say that the fact that the field carries energy & ...
2
votes
1answer
195 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
1
vote
0answers
68 views

Evaluation of the anomalous dimensions of fields in SUSY $SU(5)$

The general formula for the anomalous dimension can be found in Martin΄s review article (hep-ph/9709356), on page 62 relation (6.5.4). In the case of $SU(5)$ and especially in the paper of Kobayashi, ...
4
votes
3answers
295 views

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 ...
1
vote
0answers
50 views

Intuition behind $U(1)$-gauge model of Electrodynamics in a general spacetime

As the article Electrodynamics in general spacetime greatly explains, the $U(1)$-gauge theory is a good base for working in non-simply connected spaces. But I wonder whether there is a deep reason to ...
64
votes
4answers
6k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
2
votes
1answer
77 views

Coupling of matter field with gauge boson and Goldstone boson:

What's the fundamental difference between the way a gauge boson gets coupled to a matter field, preferably a Fermionic field and the way a Goldstone boson gets coupled to the matter field ? In ...
2
votes
0answers
30 views

Is global gauge symmetry really a symmetry and local conserved current in gauge theories?

One way to define a gauge theory is that whenever the Lagrangian is invariant under some local transformations, we say these local transformations are local gauge transformations and the theory is a ...
11
votes
1answer
469 views

What is (meant by) a non-compact $U(1)$ Lie group?

In John Preskill's review of monopoles he states Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic U(l)em gauge group ...
1
vote
0answers
20 views

Non-minimal coupling (Pauli Coupling) of gauge field with a non-relativistic scalar field

I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + ...
7
votes
1answer
215 views

Intersecting Wilson loops in 2D Yang-Mills

I am currently trying to understand 2D Yang-Mills theory, and I cannot seem to find an explanation for calculation of the expectation value of intersecting Wilson loops. In his On Quantum Gauge ...
3
votes
1answer
63 views

What are the definition and examples of topological excitation?

I read topological excitation in wiki, while it's too brief. What is the precise definition of topological excitation? And can give me some examples and explain why they are topological excitation? ...
8
votes
1answer
196 views

Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?

I seem to be missing something regarding why Yang-Mills theories are Lorentz invariant quantum mechanically. Start by considering QED. If we just study the physics of a massless $U(1)$ gauge field ...
6
votes
1answer
115 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?
1
vote
1answer
103 views

How can we derive the gauge field Lagrangian?

I learned the gauge field Lagrangian is given in this form: $$\mathcal{L} = -\frac{1}{4} \mathrm{Tr}(F_{\mu \nu}F^{\mu \nu}).$$ But how one can derive this equation starting from defining the ...
4
votes
0answers
127 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
1
vote
1answer
40 views

What are Maximally Helicity Violating (MHV) Amplitudes?

Definition of MHV amplitudes on Wikipedia: In theoretical particle physics, maximally helicity violating amplitudes are amplitudes with n external gauge bosons, where n-2 gauge bosons have a ...
0
votes
0answers
24 views

Can we use combined symmetry to simplify the calculation of algebraic PSGs?

In classifying mean-field spin liquids under projective construction, the algebraic projective symmetry group (PSG) approach focus on the mathematical construction of the possible extensions of the ...
6
votes
2answers
84 views

Why the extra term $\frac{1}{2}(\partial_{\rho}A^{\rho})^2$ in the photon Lagrangian?

In my quantum field theory class we have been told to use this Lagrangian for the photon field $$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta} -\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$ but ...
5
votes
2answers
356 views

What is a gauge in a gauge theory?

As I study Jackson, I am getting really confused with some of its key definitions. Here is what I am getting confused at. When we substituted the electric field and magnetic field in terms of the ...
3
votes
2answers
111 views

Showing that Coulomb and Lorenz Gauges are indeed valid Gauge Transformations?

I'm working my way through Griffith's Introduction to Electrodynamics. In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric ...
3
votes
2answers
112 views

Landau level degeneracy in symmetry gauge, finite system

As we know, Landau level degeneracy in a finite rectangular system is $\Phi/\Phi_0$, where $\Phi=BS$ is the total magnetic flux and $\Phi_0=h/q$ is the flux quanta. This can be easily derived using ...
3
votes
2answers
162 views

Proof of quantization of magnetic charge of monopoles using homotopy groups

Suppose we place a monopole at the origin $\{{\bf 0}\}$, and the gauge field is well-definded in region $\mathbb R^3-\{0\}$ which is homomorphic to a sphere $S^2$. Then the total manifold is $U(1)$ ...
2
votes
0answers
81 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
0
votes
1answer
43 views

SU(2) kinetic term as a trace

Is there a easy way to rewrite the SU(2) kinetic term as a trace? As in $$\mathcal{L} = -\frac{1}{4}\vec{F}_{\mu\nu}\vec{F}^{\mu\nu}\\[1cm] = -\frac{1}{2}\mathrm{tr}\Bigg[\bigg(\vec{F}_{\mu\nu}\cdot ...
2
votes
2answers
62 views

Covariant derivative applied to a vector vs. applied to a matrix?

I know there are (say) two different definitions/representations of the covariant derivative: one is the covariant derivative applied to a vector $F$, which reads as $$DF=\partial F+iAF$$ ...
4
votes
3answers
95 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
2
votes
1answer
64 views

Gauge SU(2) with real triplet

I have come across a model of gauge $SU(2)$ with a real triplet. The covariant derivative for $SU(2)$ complex doublet is written as $$D_\mu=\partial_\mu-igT^aA^a_\mu$$ where $T^a$ are generators of ...
2
votes
1answer
87 views

What is the four-dimensional representation of the $SU(2)$ generators?

Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress. I am trying to extend the Dirac field ...
3
votes
1answer
119 views

What is conformal gauge?

I often see in physics articles on gravity such notion as conformal gauge and Weyl transformation. They use Conformal gauge to change coordinates to transform metrics from arbitrary $$ds^2=g_{\mu ...
6
votes
2answers
121 views

Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
0
votes
0answers
57 views

Does the Noether's theorem apply to local symmetries? [duplicate]

Does the Noether's theorem apply to local symmetries? If yes, what is the conserved current in presence of the Gauge field $A_\mu$? I mean the conserved current is give by ...
3
votes
1answer
75 views

How to see the ground state degeneracy (GSD) from a $BF$ theory in $2+1$ $d$?

I have seen many times the $BF$ theory has non-trivial ground state degeneracy (typically on torus), but I can not see how the conclusion come out. Recently I found a paper by Hansson, Oganesyan and ...
3
votes
1answer
49 views

The differences of R parity and $U(1)_R$ symmetry

I know that we introduce R-parity to avoid proton decay. But some papers introduce $U(1)_R$ Lepton Number, e.g claudia, thomas. I have questions 1.What is the differences of R parity and $U(1)_R$? ...
0
votes
0answers
38 views

Massive gauge string sigma model action

I want to know how to insert massive gauges in string sigma model action. For massless fields it is possible by integrating the U(1) field over the string worldsheet, but in the case of massive gauge ...
2
votes
1answer
87 views

Are the Yang-Mills equation and its generalization gauge invariant?

I have derived the Yang-Mills equation and its generalization coupled to a current of a scalar field $\phi$ by extremalizing the action describing a $\mathrm{SU}(2)$ scalar field gauge theory: ...
1
vote
0answers
36 views

What is the difference between the compact U(1) group and non-compact U(1) group? [duplicate]

Is compact $U(1)$ and non-compact $U(1)$ just two different representations for the same group or the same gauge theory? If not, what the difference of them? Or are there any properties that are ...
2
votes
1answer
54 views

D-brane book-keeping and non-abelianity

In Becker's book String Theory and M-Theory in the chapter about T-duality and D-brane (Chapter 6) the following comment is made The Chan–Paton factors associate $N$ degrees of freedom with each ...
4
votes
0answers
41 views

What is the status of gauged gravity [duplicate]

The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory. We might be able to quantize gravity similarly. ...
3
votes
1answer
118 views

Clarifications needed on Gauge Fixing and Ghosts [closed]

The first time some kind of gauge fixing appears is during the Gupta-Bleuler procedure, which is used to be able to quantize the photon field: The basic gauge invariant Lagrangian leads to $\Pi_0=0$ ...
8
votes
2answers
505 views

Why do Faddeev-Popov ghosts decouple in BRST?

Why do Faddeev-Popov ghosts decouple in BRST? What is the physical reason behind it? Not just the mathematical reason. If BRST quantization is specifically engineered to make the ghosts decouple, how ...
4
votes
1answer
81 views

Two expressions for topological instanton number

I have begun to study instantons and I have the following difficulty: $\newcommand{tr}{\operatorname{Tr}}$ I am considering theory with $SU(2)$ gauge group: $S=\frac{1}{2g^{2}}\int \tr ...
1
vote
0answers
31 views

Connection between Gauge Fixing Term and Gauge Condition [duplicate]

In Peskin on page 514, when deriving the Faddeev-Poppov ghosts, they arrive at the full Lagrangian for Yang-Mills: $$ \mathcal{L} = -\frac{1}{4}F^2 + \frac{1}{2\xi} (\partial \cdot ...
13
votes
1answer
423 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 ...
0
votes
0answers
80 views

Gauge invariance in arXiv:1406.1804

I am reading the paper arXiv:1406.1804. I don't show that the invariance of the connection under the gauge transformation (2.48), I have written an email to the authors about this question. However, ...