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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6
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1answer
262 views

Wightman axioms and gauge symmetries

I have a basic understanding of the Wightman axioms for QFT. I was reading the about the Mass Gap problem for simple compact gauge groups and was wondering how the gauge group is supposed to be ...
3
votes
1answer
295 views

Vector potential $A$ on a 2-sphere $S^2$ of radius $R$ with some points removed

I am preparing myself for an exam and I got stuck with the following problem. If I wanted to calculate the vector potential $A$ on a sphere (not off or in), where some points are removed, how would I ...
2
votes
1answer
72 views

How does a gauge theory probe a spacetime singularity?

Within the framework of string theory, I have read in numerous articles such as the introduction of this this in which it is stated that the gauge theories living on a stack of D-branes can be used to ...
5
votes
0answers
105 views

(coordinates) Invariance/Covariance of Chern-Simons theory and Yang-Mills theory

It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: $$ A \wedge dA + (2/3) A \wedge A \wedge A $$ while the 4D Yang-Mills(Y-M) theory has the ...
2
votes
2answers
637 views

Polarization vectors of massive and massless particles

I read from Mandl & Shaw that when quantizing massless vector particles such as photons in Lorentz gauge, there are 4 linearly independent polarization vectors (2 of them being able to "gauged ...
8
votes
2answers
350 views

How to prove quantum N=4 Super-Yang-Mills is superconformal?

I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations Also, does a non-perturbative proof exist?
2
votes
0answers
71 views

gravitational field as a spin 2 particle using gauge invariance [closed]

can someone help me prove that a gravitational field corresponds to a spin 2 particle using gauge invariance. i know about the tensor formulation of GTR and the gauge invariance in electrodynamics ...
1
vote
0answers
114 views

Why Liouville theory is interesting? [closed]

What makes Liouville theory subject to relatively intense research field?
3
votes
1answer
244 views

What is a covariant derivative in gauge theory?

I've been studying electroweak theory and you need to keep the Lagrangian covariant by introducing covariant derivatives. What is a covariant derivative? And what does it mean to keep the Lagrangian ...
11
votes
1answer
277 views

**Group structure** in Chern-Simons theory?

A non-Abelian Chern-Simons(C-S) has the action $$ S=\int L dt=\int \frac{k}{4\pi}Tr[\big( A \wedge d A + (2/3) A \wedge A \wedge A \big)] $$ We know that the common cases, $A=A^a T^a$ is the ...
9
votes
1answer
266 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
5
votes
1answer
205 views

How do non-transverse photon polarizations cancel in Euclidean QED?

First, recall how to write scattering amplitudes in covariant fashion in Minkowskian QED. One starts by considering some process with an external photon whose momentum is chosen to be ...
0
votes
0answers
61 views

Explanation of the classical coupling of the Higgs Field to Electromagnetism

I'm interested in learning about the classical coupling of the Higgs Field to Electromagnetism. There are numerous sources explaining the Higgs mechanism quantum mechanically, i.e. How does the Higgs ...
1
vote
0answers
90 views

Why is the following gauge transformation singular?

Suppose I have a single particle Hamiltonian: $H=\frac{p^2}{2m}+\frac{\hbar k_0}{m}\vec{\sigma}\cdot\vec{p}$, either for boson or fermion. I do a gauge transformation ...
13
votes
2answers
323 views

Normalization of the Chern-Simons level in $SO(N)$ gauge theory

In a 3d SU(N) gauge theory with action $\frac{k}{4\pi} \int \mathrm{Tr} (A \wedge dA + \frac{2}{3} A \wedge A \wedge A)$, where the generators are normalized to $\mathrm{Tr}(T^a ...
2
votes
0answers
82 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
3
votes
0answers
125 views

Moduli Space of $\mathcal{N}=4$ SYM on $\mathbb{R} \times S^3$

When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space ...
4
votes
2answers
217 views

Local guage symmety implies causality

I read in a QFT book that local gauge symmetry implies causality. Could someone please explain that statement and why it's true? Thank you.
1
vote
1answer
83 views

Gauge fields in 2d spacetime

I believe it is only a technical question. However I cannot realize it. It is said in 2d spacetime the gauge fields $A_\mu$ can be rewritten in lightcone coordinates as $A_+=ig\partial_+g^{-1}$ and ...
16
votes
2answers
401 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...
1
vote
1answer
43 views

High-energy scattering matrix a become wilson line

I would like to ask why the scattering matrix $S^{ab}(x)=\left\langle gluon\: b|gluon\: a\right\rangle$ can be approximated for fast particle interacting with a traget field $A^{-}$ by wilson line ...
3
votes
2answers
276 views

Why does the $\pi$-flux state have time-reversal symmetry?

It's known that the $\pi$-flux state of the antiferromagnetic Heisenberg model on the square lattice is an important concept. The $\pi$-flux state is described by the (simplified) mean-field ...
4
votes
0answers
125 views

Noether current for the Lagrangian without Lorentz invariance

I am reading an article by Watanabe & Murayama. It gives a proof on the counting of Nambu–Goldstone bosons without Lorentz invariance. I am trying to derive all the equations to get a better ...
1
vote
0answers
44 views

Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
1
vote
1answer
128 views

Lorenz gauge in the Gupta-Bleuler Method

Greiner in his book Field Quantization page 180 & 181 wrote: As shown in (7.24) the Lorenz condition cannot be enforced as an operator identity. Instead we will use it as a condition for the ...
2
votes
0answers
41 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
1
vote
1answer
198 views

Phase shift in electromagnetic potential

In Aharonov-Bohm effect, how to derive that the wave function of a electric charge $q$ acquires a phase shift $\phi=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x}$ after travelling in the non-zero ...
5
votes
1answer
203 views

Gauge invariance and Bohm-Aharonov effect

I am confused with the Bohm-Aharonov effect: though quantum mechanics is said to be gauge invariant, the presence of a solenoid imposes a gauge. I used to think that a phase shift did not change ...
4
votes
1answer
207 views

How would one expect a massive graviton to behave?

Typically, adding a mass $m$ to a gauge boson causes the boson to only be able to travel over a finite distance, $L\sim m^{-1}$, limiting the range of the associated force. For example, photons ...
3
votes
2answers
211 views

Under which representation of U(1) transform electron and photon gauge field?

I know that under $SU(2) \times SU(2)$, the left-handed electron transforms under $ ( \frac{1}{2},0 ) $ representation and the vector gauge field $A_\mu$ under $ ( \frac{1}{2},\frac{1}{2}) $. Since ...
6
votes
2answers
192 views

How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of Poincarè symmetry, in direct ...
1
vote
0answers
34 views

The definition of Gauge Fluctuation

What is the definition of Gauge Fluctuation? For example, in Z2 lattice gauge theory. Thanks.
6
votes
0answers
101 views

Does the inverse of the Dirac conjecture hold?

In the theory of constrained Hamiltonian systems, one differentiates between primary and secondary constraints, where the former are constraints derived directly from the Hamiltonian in question and ...
4
votes
1answer
169 views

Conserved topological charge for d=3 Yang-Mills. G=U(2)

Consider a pure Yang-Mills lagrangian density $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu}$$ with gauge group $U(2)$. Take the generators for $U(2)$ to be $t_0$, $t_i \ i=1,...,3$ with ...
3
votes
1answer
408 views

Noether First and Second Theorem

I have this question related to the the Noether's Theorems. I want to know a rigorous enough enunciation of this theorem, the context is Classical Field Theory without fancy geometrical structures ...
2
votes
1answer
120 views

Hyperkahler manifolds and their use in theoretical physics

Just as the title says: What is the easiest definition of a Hyperkahler Manifold? Could you give some examples of Hyperkahler manifolds, and manifolds which fail to be hyperkahler? Why are such ...
3
votes
1answer
209 views

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite?

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite? Let's say the gauge group is a nonabelian simple Lie group G. Suppose ...
3
votes
0answers
93 views

Do primary first class constraints change the electric field in the Hamiltonian form of Maxwell's theory?

In my understanding of Dirac's theory of constrained Hamiltonians, the primary (and also the secondary) first class constraints are generators of canonical transformations that do not change the ...
6
votes
2answers
261 views

Is the Green function a prescription for a connection?

I'm trying to learn connection on principal fibre bundle. As far as I can see, the connection is just a given prescription for the displaced field/function on the base space to remains on the ...
1
vote
1answer
61 views

Gradient of the potential originated from two similar magnetic vector potentials is not the same

The magnetic vector potential $\textbf{A}$ can be defined up to a gradient of a field. Adding or subtracting such gradient should not change the physics of the problem. The same reasoning is applied ...
0
votes
0answers
85 views

What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge ...
3
votes
1answer
140 views

Ghost Number Conservation

I've been reading about gauge theory quantization, and understand it mostly. The only thing I don't get is why people talk about "ghost number conservation". As far as I can tell, the ghost number is ...
3
votes
1answer
209 views

A naive question on the Quantum Hall Effect(QHE) and the confinement in gauge theory?

The non-interacting 2D lattice QH system is described by the Hamiltonian $H=\sum t_{ij}e^{iA_{ij}}c_i^\dagger c_j+H.c$ My confusion is: Does this imply that the $2D$ lattice QHE is described by the ...
2
votes
0answers
115 views

Is the $SU(2)$ flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?

The $SU(2)$ flux defined in the context of PSG is as follows: Consider the mean-field Hamiltonian $H_{MF}=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ description of a 2D lattice spin-model, the ...
2
votes
1answer
221 views

A naive question on the $U(1)$ gauge transformation of electromagnetic field?

For simplicity, in the following we set the electric charge $e=1$ and consider a lattice spinless free electron system in an external static magnetic field $\mathbf{B}=\nabla\times\mathbf{A}$ ...
1
vote
2answers
296 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
2
votes
2answers
242 views

Two puzzles on the Projective Symmetry Group(PSG)?

Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's paper. To present the questions clearly, imagine that we use the Shwinger-fermion ...
1
vote
2answers
355 views

Gauge theory in classical electromagnetism

I understand gauge theory as the theory of continuous transformation group which keeps Lagrangian (or dynamics) invariant. So some integral invariants could be found. In terms of classical ...
3
votes
1answer
108 views

Are the symmetry operators well defined in the context of Projective Symmetry Group(PSG)?

Consider the Schwinger-fermion approach $\mathbf{S}_i=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$ to spin-$\frac{1}{2}$ system on 2D lattices. Just as Prof.Wen said in his seminal paper on PSG, the ...
11
votes
3answers
1k views

Is it really proper to say Ward identity is a consequence of gauge invariance?

Many (if not all) of the materials I've read claim Ward identity is a consequence of gauge invariance of the theory, while actually their derivations only make use of current conservation ...