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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3answers
181 views

About constraints of the first class and electrodynamics

Consider a theory in the Hamiltonian formalism and assume that it has constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx 0$ of ...
5
votes
1answer
169 views

How will SR EM Lagrangian change if we find a magnetic charge?

When we introduce electromagnetic field in Special Relativity, we add a term of $$-\frac e c A_idx^i$$ into Lagrangian. When we then derive equations of motion, we get the magnetic field that is ...
4
votes
2answers
181 views

Wess-Zumino Gauge in non-Abelian supersymmetric theory

I've got a question concerning non-Abelian supersymmetric gauge theories. Consider supersymmetric non-Abelian theory realized on chiral superfields $\Phi_i$ in a representation $R$ with matrix ...
1
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1answer
69 views

In what sense are photons emergent?

Recently I read in an essay by Wilczek: "Photons are mixtures of weak B3 and hypercharge C mesons. It is those objects, not the emergent photon, whose properties are ideally simple." Until now I ...
1
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1answer
43 views

What does “local composite symmetry” mean in ${\cal N}=8$ $d=5$ supergravity?

What does it mean "local composite symmetry" in supergravity? Specifically, I don't understand very well the local composite symmetry ${\rm USp}(8)$ in ${\cal N}=8$ $d=5$ supergravity.
1
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1answer
41 views

Volume factor in Faddeev-Popov quantisation

In Faddeev-Popov quantisation, why does the integral over gauge parameter cancel the volume factor of the gauge group that's in the denominator? In fact, I don't understand where the volume factor ...
2
votes
0answers
47 views

Quivers Representations in SUSY gauge theories

I would like to hear some reasons and ideas on how quivers are useful in SUSY gauge theories. There is a nice answer about the case of D-branes here but it is not clear on their appearance in gauge ...
1
vote
1answer
72 views

If isospin is conserved under strong interactions why it is represented by SU(2)?

As far as I know from my readings SU(2) is a representation group of isospin symmetry which shows deep symmetry of the strong force which conserves flavor. Isospin symmetry is broken under weak ...
1
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1answer
76 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses ...
2
votes
1answer
55 views

In which contexts are gauge theories applied?

According to the book Quantum Field Theory for the Gifted Amateur, on page 128 they say A theory which had a field $A^\mu(x)$ introduced to produce an invariance with respect to local ...
1
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1answer
69 views

Generalized spin connection and dreibein in higher spin gravity

I am studying 3D higher spin gravity and I would like to know the mathematical and physical meaning of generalized spin connection and generalized dreibein that appear in this theory. It is well known ...
1
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2answers
83 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 ...
1
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1answer
86 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
1answer
57 views

Counting d.o.f. and gauge fixing $A_{\mu}$ and $\psi$ in $D$-dimensions

Setup: Let us assume we are in $D$-dimensional Minkowski space-time where $D=d+1$. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy $$\partial_{\mu}F^{\mu \nu}=0 ...
5
votes
2answers
201 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 ...
11
votes
3answers
255 views

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 ...
9
votes
1answer
916 views

Why should bosons be in the adjoint representation of the gauge group?

Is there a deep mathematical reason for why bosons should be in the adjoint representation of the gauge group rather than any other representation?
4
votes
1answer
371 views

What is the fundamental representation in field theory?

In field theory we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to ...
4
votes
0answers
56 views

Reality of the action in QFT

Following Ramond, 1.5 Field Theory, it is mentioned that the classical Lagrangian density in (workable for HEP) QFT theories has to be Real, otherwise total probability is not conserved. Can someone ...
7
votes
2answers
533 views

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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0answers
93 views

Expressing the gauge field strength tensor in terms of covariant derivatives of the vector potential

Writing the covariant derivative as $$ \tag{1} D_\mu = \partial_\mu -ig A_\mu $$ it is easy to show that (in the non-abelian case) $$ \tag{2} [D_\mu,D_\nu] = -ig (\partial_\mu A_\nu - \partial_\nu ...
6
votes
1answer
85 views

Substitution $\partial_\mu \to D_\mu \equiv \partial_\mu + ieA_\mu$ allows the introduction of electromagnetic interactions [duplicate]

I want to show that the substitution $\partial_u \to D_\mu \equiv \partial_\mu + ieA_\mu$, or equivalently $p_\mu \to p_\mu - eA_\mu$ allows the introduction of electromagnetic interactions. Here $e$ ...
3
votes
0answers
69 views

Substitution $\partial_\mu \to D_\mu \equiv \partial_\mu + ieA_\mu$ allows the introduction of electromagnetic interactions [closed]

I want to show that the substitution $\partial_u \to D_\mu \equiv \partial_\mu + ieA_\mu$, or equivalently $p_\mu \to p_\mu - eA_\mu$ allows the introduction of electromagnetic interactions. Here $e$ ...
3
votes
0answers
147 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 ...
1
vote
0answers
56 views

What's the physical or mathematical meaning of considering non-minimal coupling?

Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of ...
5
votes
3answers
849 views

Potential energy in Special Relativity

In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what ...
5
votes
2answers
150 views

Why is it important that the vector current should be conserved in QED?

In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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votes
0answers
32 views

Why is there an Euler density in SCFT $T_{\mu}^{\nu}$?

The super conformal field theories are above all conformal. Conformal theories are defined on flat space-times. Despite that, if one looks at the stress tensor trace of a SCFT in 4d you get a ...
1
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0answers
76 views

Why $D^{\mu} D^{\nu} F_{\mu \nu}=0$ ? (Noether Identity) [closed]

I have to show that: $$D^{\mu} D^{\nu} F^A_{\mu \nu}=0$$ vanish identically. This is the generalization to non Abelian groups of $\partial^{\mu} \partial^{\nu} F_{\mu \nu}=0$, apparently called ...
-1
votes
1answer
61 views

How one can know the gauge field emerging from the local gauge invariance is actually the EM field? [closed]

How one can know the gauge field emerging from the local gauge invariance is actually the EM field? I understood in a simple scalar field whose Lagrangian is given by $ \mathcal{L} = ...
1
vote
0answers
53 views

Proving a relation for representations of gauge groups [closed]

I have asked this question in Math Stackexchange as well. However, given that it is closely related to gauge theories studied by physicists who will probably be more familiar with the language and ...
8
votes
2answers
403 views

The gauge covariant derivative and its 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 ...
6
votes
2answers
169 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 ...
2
votes
1answer
111 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 ...
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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 ...
1
vote
0answers
88 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, ...
7
votes
3answers
491 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 ...
2
votes
0answers
78 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 ...
2
votes
0answers
89 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 ...
2
votes
0answers
55 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
332 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
89 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? ...
6
votes
1answer
134 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
151 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 ...
5
votes
0answers
146 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
84 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 ...
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votes
0answers
47 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 ...
8
votes
2answers
138 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
497 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
552 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 ...