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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12 views

General framework of Supersymmetry

Even the people who are skeptical about SUSY are happy with the SUSY searches going on at LHC because they recognize that SUSY's general framework is quite flexible and the search strategy used in ...
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1answer
33 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 ...
3
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1answer
116 views

BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
6
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1answer
435 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 ...
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0answers
100 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.)
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1answer
58 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
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1answer
57 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
90 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 ...
3
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1answer
266 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 ...
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2answers
93 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 ...
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1answer
129 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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1answer
31 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
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1answer
64 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
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1answer
69 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 ...
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0answers
151 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 ...
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1answer
67 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 ...
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4answers
1k 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 ...
7
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1answer
342 views

Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?

The compact U(1) lattice gauge theory is described by the action $$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$ where the gauge connection $A_l\in$U(1) is defined ...
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1answer
161 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 & ...
4
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0answers
61 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 ...
2
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0answers
61 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
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0answers
158 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
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1answer
266 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 ...
43
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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 ...
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0answers
177 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 ...
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1answer
98 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
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1answer
60 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 ...
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2answers
539 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 ?
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1answer
323 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 ...
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0answers
21 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 ...
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0answers
24 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) ...
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0answers
38 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?
1
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1answer
37 views

Derivation of Aharanov Bohm effect for Quasiparticles

I've noticed the following: Observation: Central results in the condensed matter physics rely on Ahranov Bohm-type arguments involving quasiparticles with fractional charge. However, I can't ...
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0answers
28 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
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1answer
886 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
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1answer
27 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
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1answer
185 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 ...
9
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0answers
139 views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
3
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3answers
157 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 ...
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0answers
14 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 ...
1
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2answers
65 views

Why can the divergence of vector potential be anything?

Purcell in his book was deriving the vector potential $\bf A$ using $\text{curl}\;(\text{curl}\; \mathbf A)= \mu_0 \mathbf J\; .$ After some algebra, he came to this: $$-\frac{\partial^2 ...
5
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0answers
146 views

Gauge potential for locomotion at low Reynolds number

I've been studying some approaches with gauge theory to some problems in Mechanics and I've found the problem of self propulsion at low Reynolds number a quite complicated one. The approach I'm asking ...
1
vote
1answer
113 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
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0answers
21 views

What exactly is the “diagonal embedding” in the supersymmetric topological twist?

Consider $\mathcal{N}=2$ pure SYM theory. If we want to put the theory in a 4-manifold we take its topological twist. The global symmetry group $$G= SU(2)_{+} \times SU(2)_{-} \times SU(2)_I \times ...
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0answers
22 views

References for the non-Abelian gauge covariant Laplace equation?

Is there a standard reference which discusses solutions to the non-Abelian gauge covariant Laplace equation $D_{\mu} D^{\mu} \phi = 0$, where $D_{\mu} \phi = \partial_{\mu} + ig[A_{\mu}, \phi]$? Note ...
3
votes
1answer
108 views

How can I understand instantons as sheaves?

In specific, instantons are considered or interpeted as torsion free coherent sheaves. Why is that the case? Is there a nice way to understand this relation and of course also understand how the two ...
1
vote
1answer
79 views

Gauge the symmetry $φ \to φ + a(x)$ for a free massless real scalar field

How does one alter the Lagrangian density for a real scalar field $$\frac{∂_μφ∂^μφ}{2}$$ such that is will be invariant under the gauge transformation $φ → φ + a(x)$? For a complex scalar field ...
1
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0answers
61 views

Unitary gauge transformation [closed]

I have the Hamiltonian of a charged particle without Spin in a time- independent magnetic field and an external Potential (no electric field). Also I have the standard Gauge-Transformation $A ...
2
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0answers
48 views

Why does a Gauge group have to be a compact Lie group? [duplicate]

In Topological Solitons by Nicholas Manton where he considers "compact Lie groups" to be the gauge groups for generalizing gauge theoretic concepts. But, he does not mention why that condition is ...
3
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2answers
163 views

Gauge theory for mathematicians?

I'm looking for a textbook or set of lecture notes on gauge theory for mathematicians that assumes only minimal background in physics. I'd prefer a text that uses more sophisticated mathematical ...