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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7
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2answers
823 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 ...
1
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0answers
50 views

Why Dirac monopole is a topological defect in a $U(1)$ gauge theory? [duplicate]

How does $U(1)$ gauge group at long distances, give rise to magnetic monopoles? Also why is it said that Dirac monopole is a topological defect in a compact $U(1)$ gauge theory?
18
votes
1answer
761 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
1
vote
1answer
59 views

Why group elements associated with gauge transformations of finite action field configurations in QCD don't depend in $r$?

I am reading the chapter on instantons in Coleman's Aspects of Symmetry. I am puzzled by an argument i don't quite follow. In section 3.2, Coleman considers configurations of the gauge field with ...
0
votes
1answer
52 views

Uniqueness of the magnetic vector potential?

I am trying to find the magnetic vector potential a distance of $s$ (cylindrical radial variable) from an infinite wire carrying current $I$. The magnetic field at a distance $s$ from a wire is ...
17
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2answers
1k views

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

In John Preskill's review of monopoles he states on p. 471 Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic $U(l)_{\rm ...
0
votes
1answer
55 views

Integrals of Chern class, $c_i$ in YM theories

I am a bit confused with the definition of the 1st (and 2nd by extension) Chern class in YM theories. I understand that in general $c_i \in H^{2i}(M,\mathbb{Z})$ where $M$ is a smooth manifold. Then, ...
3
votes
1answer
2k views

Minimal vs. Non-minimal coupling in General Relativity

What is the difference between Minimal vs. Non-minimal coupling in General Relativity? A brief introduction to Minimal Coupling in General Relativity could be useful too.
2
votes
1answer
114 views

Why only gauge transformations in electromagnetism?

first of all, I need to say that I'm a mathematician, so this question may sound a little stupid. Keeping this is mind, please, try to use coordinate-free notations. Along this question, I will use ...
4
votes
1answer
241 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 ...
7
votes
1answer
1k views

Counting degrees of freedom for gravitational waves as a gauge field

Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...
5
votes
3answers
167 views

Spontaneous symmetry breaking to subspace not giving massless bosons

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

Homogenuous Maxwell Equations in the Language of Differential Forms

I understand that if I define electric field to be $E=E_i dx^i$, magnetic field to be $B=B_1 dx^2 \wedge dx^3 + B_2 dx^3 \wedge dx^1 + B_3 dx^1 \wedge dx^2 $, and field strength to be $F= dx^0 ...
13
votes
3answers
3k views

Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or ...
0
votes
1answer
78 views

Gauge transformations in gravity [duplicate]

The Maxwell equations are invariant under the transformation $$A_{\mu} \rightarrow A_{\mu} - \dfrac{1}{e}\partial_{\mu}\alpha(x)$$ where $\alpha(x)$ is a phase transformation varying from point to ...
2
votes
2answers
159 views

Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )

I'm trying to understand the way that the Higgs Mechanism is applied in the context of a $U(1)$ symmetry breaking scenario, meaning that I have a Higgs complex field ...
1
vote
0answers
68 views

Good Books on Gauge Theory [duplicate]

Possible Duplicate: Comprehensive book on group theory for physicists? I'm having a hard time trying to get my head around the fundamentals of gauge theory. I've taken classes in QFT and ...
0
votes
1answer
41 views

Counting number of degrees of freedom in constrained system

Following Counting degrees of freedom in presence of constraints, we know that there would be N-2M-S dofs if we have M 1st-class constraints and S 2nd-class constraints in N-dim phase space. I don't ...
0
votes
1answer
38 views

To which type of particles gauginos are supposed to couple?

I wonder about to which type of particles gauginos couple in general. I admit my knowledge in supersymmetry is very limited. Let's take an example: The photino. If it behaved similar to the photon, it ...
6
votes
1answer
456 views

What exactly is the connection between gauge transformations and symmetry groups?

For a given gauge transformation, say, the electromagnetic field, where observable quantities aren't affected by transformations of the form $$\mathbf{A}' = \mathbf{A} + \nabla \chi,$$ $$\phi' = \phi ...
0
votes
0answers
102 views

Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]

Similar to this reference, are there more such references / works [including textbooks] available in the literature? (A list would be greatly welcomed and appreciated.)
3
votes
1answer
72 views

Is this a valid Gauge fixing condition?

I've been given the following gauge fixing condition: $$A_\mu A^\mu = 0 $$ And I've been asked to show if it is a valid gauge fixing condition or not. I believe that it isn't because I've already ...
3
votes
1answer
67 views

What is the gauge group of eletromagnetism?

Gauge transformations allowed by physical theories form groups. For example, a wave function in quantum mechanics can be multiplies by $e^{i\theta}$ and this won't change a thing. So the gauge group ...
4
votes
2answers
95 views

Anomalous Slavnov-Taylor identity

I will be happy if someone could clarify the mystery here. Consider the following derivation of the anomalous Slavnov-Identity. It's based on lecture notes by Adel Bilal. Suppose we have an action ...
1
vote
2answers
117 views

Chern-Simons theory

The Chern-Simons 3-form is given by $\omega_3={\rm Tr} \left[ A\wedge dA+\frac{2}{3}A\wedge A\wedge A\right]$ where $A$ is a connection one-form in the adjoint representation of a non-Abelian gauge ...
1
vote
1answer
37 views

General principles require that a massless vector couple to a conserved current?

I have a quote from Introduction to Bosonic Strings by Polchinski on page 28 which is presented below: "General principles require that a massless vector couple to a conserved current and ...
3
votes
1answer
74 views

Fayet-Iliopoulos terms

It is mentioned in first page of this paper by Seiberg and Komargodski that the Lagrangian in superspace of a $U(1)$ gauge SUSY theory with FI terms is not gauge invariant. However, the FI terms in ...
2
votes
1answer
88 views

What symmetry gives you charge conservation?

This is a popular question on this site but I haven't found the answer I'm looking for in other questions. It is often stated that charge conservation in electromagnetism is a consequence of local ...
1
vote
0answers
173 views

How should we understand the value of a recent theory published on Phys. Rev. D? [closed]

I would like to know what to make of this paper, published on Phys. Rev. D on the 11$^{th}$ of January: Quantum field theory of gravity with spin and scaling gauge invariance and spacetime ...
0
votes
1answer
92 views

Local and global U(1) gauge symmetries of Hamiltonian

This question is about understanding the basic ideas behind gauge transformations as I am fairly new to this! I learned that the Hamiltonian is invariant under global U(1) gauge transformations ...
5
votes
4answers
2k views

Degrees of freedom of the graviton versus classical degrees of freedom

I have a puzzle I can not even understand. A graviton is generally understood in $D$ dimensions as a field with some independent components or degrees of freedom (DOF), from a traceless symmetric ...
4
votes
0answers
72 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
3
votes
0answers
76 views

Classical electrodynamics as an $\mathrm{U}(1)$ gauge theory

Preface: I haven't studied QED or any other QFT formally, only by occasionally flipping through books, and having a working knowledge of the mathematics of gauge theories (principal bundles, etc.). ...
6
votes
0answers
185 views

$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is ...
2
votes
1answer
277 views

Entanglement entropy for $U(1)$ lattice gauge theory

Can someone please let me know if there is some reference for the calculation of entanglement entropy of $U(1)$ lattice gauge theory? I have seen a few references where Z2 lattice gauge theory has ...
46
votes
0answers
2k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
0
votes
0answers
195 views

Why does electromagnetism have torsion, whereas gravity does not?

Why don't we use torsion-free covariant derivatives for QM, even though we already do so in the case of GR? In general relativity, we use the Levi-civita connection, a torsion-free connection ...
0
votes
1answer
115 views

Enhancing the QED $U(1)$ gauge symmetry

QED is a gauge theory based on $U(1)$ gauge symmetry, which gives rise to photon as the gauge boson mediating the interaction. Mathematically, I think it is perfectly allowed to implement a ...
3
votes
1answer
66 views

Non-perturbative effects: classical or quantum?

Are non-perturbative effects (solitons) classical or quantum effects (corrections) ? (examples ?) My confusion stems from the fact that, for instance, an instanton is a classical solution of the ...
9
votes
2answers
597 views

Gauge fermions versus gauge bosons

Why are all the interactions particle of a gauge theory bosons. Are fermionic gauge particle fields somehow forbidden by the theory ?
19
votes
1answer
359 views

What, to a physicist, are instantons and the Donaldson invariants?

I study gauge theory from a mathematical perspective. To me, one of the most fundamental ideas is the notion of an instanton on a 4-manifold. To be precise, I have a Riemannian 4-manifold and a ...
0
votes
0answers
23 views

Global and local symmetry for Isospin/Strangeness etc

Why some symmetries $ \big[SU(3),SU(2)$ and $U(1)\big]$ of the Standard Model are local, and some others remain global, like Isospin and Strangeness. Is there a fundumental reason for that? Doesn't it ...
0
votes
0answers
37 views

Expansion of comparator

Currently I am working on Pesking Schroeder Section 15.1 and trying to understand the expansion given in (15.5), which is $$ U(x+\epsilon n, x) = 1 - i\,e\,\epsilon\,n^{\mu}\,A_{\mu}(x)+O(\epsilon^2) ...
0
votes
0answers
42 views

What is the simplest chiral $U(1)$ theory that satistifies both gauge and gravity anomalies?

I've learned the chiral $U(1)$ theory that satisfies either gauge anomalies or gravity anomalies. But what's the theory satisfies both of them?
0
votes
0answers
36 views

Feynman diagrams with ghosts and symmetry breaking

Let us think of an abelian gauge theory, precisely a scalar QED with 3 complex components of the scalar field and a 4-degree auto-interaction mixing components. Let us consider a spontaneously ...
8
votes
1answer
952 views

The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
0
votes
1answer
36 views

Non-abelian gauge covariant derivative acting on non-algebra-valued quantities

How does a gauge covariant derivative in a non-abelian field theory act on various quantities which are not valued in the algebra, and why? In particular, how does it act on a scalar valued function ...
5
votes
1answer
197 views

Charged CFT observables and AdS/CFT

I have a simple question regarding the holographic dictionary when mapping operators on the CFT side to those in AdS. One piece of the dictionary is that a global symmetry maps onto a gauge symmetry ...
3
votes
3answers
171 views

Interpretation of QED gauge freedom

In quantum (or classical) electrodynamics we are free to make gauge transformations, which change the form of terms in the Feynman diagrams (or the potentials) without affecting any physical ...
0
votes
0answers
17 views

about the Horizontal Lift in a Princiapal Bundle

I'm currently studying Fibre Bundle by Nakahara's book, and I'm a bit confused about the following: Imagine we have a Principal Bundle $P(M,G)$ with open chart {$U_i$} and a local section ...