Questions tagged [gauge-theory]

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. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

Filter by
Sorted by
Tagged with
1
vote
1answer
119 views

Photon Path Integral and Lorenz Gauge

I am reading Srednicki's QFT book (http://web.physics.ucsb.edu/~mark/qft.html). In chapter 57, specifically in page 343, the book stated that there's a problem with the path integral because the ...
1
vote
0answers
43 views

How to understand the path integral of $U(1)$ gauge field under Coulomb gauge?

I want to obtain Green's function of $U(1)$ gauge field under Coulomb gauge. For some reason, I want to finish it in Euclidean space, i.e. both time-space $x_\mu$ and field strength $A_\mu$, so that ...
7
votes
3answers
236 views

How to compute gauge potential $A$ from the field strength $F$?

Let $F=dA+A \wedge A$ be the field strength that solves vaccum Yang-Mills equation. The question is: how to recover the gauge potential $A$? Is there any standard way? or any theorem stating the ...
0
votes
2answers
32 views

Variation of QED gauge missing step

I have several questions about this problem. I have been given a non-linear gauge condition for a QED theory: $$F = \partial_{\mu}A^{\mu} + \frac{\lambda}{2}A_{\mu}A^{\mu}.$$ I have found online that ...
1
vote
0answers
55 views

Non-linear QED gauge fixing, writing the effective Lagrangian

I have several questions about this problem. I have been given a non-linear gauge condition for a QED theory: $$F = \partial_{\mu}A^{\mu} + \frac{\lambda}{2}A_{\mu}A^{\mu}.$$ Then I need to write the ...
2
votes
1answer
105 views

How to find the Hamiltonian from the energy-momentum tensor for a free electromagnetic field?

This question is related to a previous question that I have asked before titled: Energy-Momentum Tensor for the Electromagnetic Feild asking why the energy-momentum tensor had the following form $$T^{...
-1
votes
3answers
129 views

Linear algebra as a gauge theory

Is linear algebra a gauge theory? Is the gauge transformation a change of basis? This was the explanation that I received: "Take the principal bundle to be the frame bundle $LM$ of your space $M$...
2
votes
1answer
185 views

Justification of the $U(1)$ gauge for electromagnetism?

Why should we expect or require that there is a $U(1)$-gauge symmetry in the theory of a charged particle (such as QED), namely that its physical properties should not change under local changes of ...
0
votes
2answers
139 views

Why $W^+$ and $W^-$ bosons counted as two types of particles? but not $e^+$ and $e^-$?

The $W^+$ and $W^-$ bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. In this sense, if we know the properties of $W^+$, we should ...
1
vote
0answers
83 views

Understanding the QED Lagrangian using Yang Mills formalism

In QED the Lagrangian is $$ \mathcal{L} = \bar{\psi}(i \not \partial - m ) \psi - \frac{1}{4} F_{\mu \nu} F^{\mu \nu} - e \bar{ \psi} \gamma^\mu \psi A_\mu $$ which is the sum of a Dirac term, the ...
5
votes
1answer
80 views

How does gauge symmetry constrain the dynamics of a field's physical degrees of freedom?

My rough understanding of gauge theory is that some of a field's degrees of freedom (d.o.f.) may turn out to be "non-physical" due to local symmetries. But does gauge symmetry constrain the ...
1
vote
1answer
43 views

Integral eigenvalues in compact rank-2 symmetric $U(1)$ gauge theory

I am reading a paper related to rank-2 symmetric $U(1)$ gauge theory: Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory (or arXiv:1802.10108). My ...
2
votes
1answer
88 views

Lagrangian density for abelian gauge theories

I'm studying abelian and non-abelian gauge theories, using the geometric approach. I have defined the generalized potential (that is the connection 1-form of the principal bundle $P(M,G)$ where $M$ is ...
2
votes
1answer
86 views

Seiberg-Witten Map Derivation

In the original paper defining the Seiberg-Witten map, I have been confused about the following step in their derivation. Using the gauge transformation constraint, they write \begin{align*} A'_i (A+ \...
1
vote
1answer
78 views

Peskin & Schroeder about spontaneous symmetry breaking

I am confused about how Peskin & Schroeder derive the matrix (21.39): \begin{equation} gF^a_{\ \ i}=\frac{v}{2} \left(\begin{array}{ccc} g & 0 & 0 \\ 0 & g & 0 \\ 0 & 0 & g ...
0
votes
1answer
92 views

Electroweak Lagrangian is not coordinate invariant?

I was reading the Wikipedia page for the electroweak Lagrangian https://en.wikipedia.org/wiki/Electroweak_interaction It looks ok to me until you get to the symmetry broken four-point self ...
0
votes
1answer
53 views

What are the physical degrees of freedom in Yang-Mills theories?

I am pretty familiar with the Lagrangian formulation of quantum electrodynamics and perturbation theory techniques; however, I am hoping to move into QCD and other Yang-Mills Theories. As I do, I am ...
0
votes
0answers
46 views

Does the fiber bundle approach for Berry connection contradict adiabatic theorem?

In Ref [1], the authors show how the Berry connection is a geometric quantity using the fiber bundle approach. My question is about the idea of taking a local section of a fiber bundle (corresponding ...
0
votes
2answers
49 views

Goldstone boson-Gauge boson coupling in the Glashow-Weinberg-Salam (GWS) model

In the GWS model it is expected to see terms like $\sim gv\partial_\mu \phi W^\mu$, where $g$ is a coupling constant, $v$ the VEV of the Higgs field, $\phi$ a Goldstone boson, and $W$ a gauge boson. ...
11
votes
2answers
330 views

Is it possible to bound a single D0-brane to a D4-brane?

I'm studying the Jafferis solution for twisted $N=4$ Yang-Mills theory in four dimensions from the paper Crystals and intersecting branes. Consider the problem of computing the charges of the allowed ...
0
votes
1answer
53 views

Finding helicity eigenstates

Question: Give the mode expansion of the $A_i$ in terms of plane wave \begin{equation} \epsilon^{\pm}_i(p)e^{-ip \cdot x} \ \ \ \ \ \text{ and } \ \ \ \ \ \epsilon^{*\pm}_i(p)e^{-ip \cdot x} \...
0
votes
0answers
52 views

How to prove that the massive gauge fields transform in the fundamental representation of the gauge group of unbroken generators?

In Chapter 84 (page 528) of Srednicki's Quantum Field Theory, he wrote Recall from section $32$ that a generator $T^a$ is spontaneously broken if $(T^a_{\scriptscriptstyle{\text{R}}})_{ij} v_j \ne 0$....
0
votes
1answer
116 views

Fix temporal gauge $A_0=f$ using an appropriate gauge transformation

Consider the Lagrangian \begin{equation} \mathcal{L}= -\frac{1}{4} F_{\mu \nu}F^{\mu \nu} - A_{\mu}J^{\mu} \ \ \ \ \text{ with } \ \ \ \ F_{\mu \nu}=\partial_\mu A_\nu - \partial_{\nu}A_{\mu}. \...
0
votes
1answer
66 views

Gauge field and Lie group

I'm studying $SU(N)$ gauge theory, but I'm confused. Here(Gauge fields -- why are they traceless hermitian?), the reason why gauge field is in Lie albgebra of gauge group $G$ is that we have to cancel ...
1
vote
1answer
72 views

The relation between gauge symmetry and global internal symmetry

I'm a little confused about the relation between the gauge symmetry and global internal symmetry of a field theory. I'd appreciate any clarification on this. My question can be phrased as the ...
1
vote
1answer
164 views

Gauge invariance and Gauss's law in $U(1)$ E&M theory

I am reading an article: Stable Gapless Bose Liquid Phases without Any Symmetry (and also see Pretko's paper on the same subject). There, the authors wrote that Gauss's laws are associated with ...
1
vote
1answer
26 views

How to determine the ground state configuration for a Hamiltonian as a function of expansion in terms of some parameter in the Hamiltonian?

I have been learning about lattice gauge theories, in particular about the Ising gauge theory on the 2D square lattice. The Hamiltonian for a system with no matter fields is given by (for eg. from ...
3
votes
1answer
91 views

Consequence of diffeomorphisms invariance in General Relativity

Let's consider a theory with gravity and matter field(s) $\Phi$. The action of this theory is the following: \begin{equation} S[g,\Phi] = S_g[g]+S_m[g,\Phi] = \frac{1}{16\pi G}\int_Md^4x\sqrt{-g}R+\...
1
vote
2answers
134 views

Functional derivative in Faddeev Popov method (Lorenz Gauge)

When applying Faddeev and Popov method (am using Peskin and Schroeder as reference), we use the identity: $$1=\int \mathcal{D}\alpha(x)\delta(G(A^\alpha)) \det\left(\frac{\delta G(A^\alpha)}{\delta\...
3
votes
1answer
65 views

Is this measure employed in the Faddeev-Popov procedure related to the Haar measure?

In the Faddeev-Popov procedure one defines the Faddeev-Popov determinant through the formula $$\int {\mathcal{D}\alpha \ } \delta\big[G(A^\alpha)\big]\Delta[A]=1,\tag{1}$$ where $G(A^\alpha)$ is the ...
3
votes
1answer
69 views

Calculations of chiral condensate (from David Tong's notes)

I got confused on the calculation of chiral condensate in David Tong's Gauge theory. The equation 3.52 reads \begin{equation} \langle\bar{\psi}_{-}\psi_{+}\rangle=\big(\prod_{n}\lambda_n\big)\frac{1}{...
1
vote
1answer
86 views

Interpretation of QED as a $U(1)$ gauge theory

Forgive me if what I’m asking is too naive for this site. I'm a math student who is recently studying electrodynamics and gauge theory myself. While I'm aware of the fact that QED can be realized as a ...
2
votes
1answer
59 views

Writing the $U(1)$ gauge transformation as coordinate transformation

In quantum mechanics one can "always" write the way an operator acts on a wave function as a coordinate transformation. As an example we can look at unitary representation of the momentum ...
0
votes
0answers
64 views

Equations of motion involving terms with four vectors

So I am trying to find equations of motion for the Lagrangian associated with a non-Abelian Gauge theory for $SU(N)$, and while I was doing the math, I was a bit confused the indices. So I have $\...
2
votes
1answer
70 views

Chemical potentials for D-brane bound states

This question is about a mathematical subtlety arising in the computation of the partition function of a supersymmetric ensemble of some lower dimensional $D$-branes attached to a stack of higher ...
1
vote
1answer
52 views

Confution on UV cut-off in the calculation of effective action and Beta function

I am reading David Tong's gauge theory notes and meet some difficulties. In section 2.4.2, he uses background field to calculate effective action $S_{eff}$ and Beta function. Simply like follows: ...
1
vote
2answers
128 views

What precisely and mathematically does it mean to say gauge bosons as elementary particles?

In standard particle physics textbook, we say that photons, gluons and $W$ and $Z$ bosons are gauge bosons as elementary particles. However the gauge bosons are vector bosons and they carry the form ...
0
votes
0answers
56 views

What precisely and mathematically does it mean to have $W$ bosons carry electric charges?

What precisely and mathematically does it mean to have $W$ bosons carry electric charges? We know from Wikipedia that experiments say that $W$ bosons carry electric charges: $W^\pm$ carry $+$ and $-$ ...
5
votes
0answers
59 views

How do you write a resolution of unity (the identity) in gauge theories?

In, say, a quantum field theory of a single scalar field $\phi$, it is common to write the identity as ${\bf 1}=\int{\cal D}\phi\, |\phi\rangle\langle \phi|$, a useful thing to do in various path ...
3
votes
0answers
39 views

How to visualize the $U(1)$ instanton event in (2+1)D compact lattice gauge field?

In the continuum limit of (2+1)-dimensional compact $U(1)$ gauge field, the instantons are input by hand in terms of nonconservation of magnetic flux $\int b$: \begin{eqnarray} \int dxdy [b(x,y,t+\...
0
votes
1answer
58 views

Derivative of a field strength tensor wrt field potential in YM gauge

I'm currently following this article to cosntruct a gauge invariant energy stress tensor for pure Yang-Mills gauge: $$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}^aF_{\mu\nu}^a, \qquad F_{\mu\nu}^a = \...
3
votes
1answer
86 views

In fiber bundle picture of Berry connection, what is the vertical basis if the horizontal basis is the underlying parameter space?

In Ref. [1], the authors show how The geometric (Berry) phase is shown to have its origin in the nontrivial geometry of the fiber bundle: Hilbert space --—> space of states. The nontrivial ...
2
votes
0answers
69 views

$(p,q)$-5 webs from $M$-Theory

The authors of the paper "Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams" consider type $IIB$ superstring theory compactified on a circle $S^{1}$ and claim (in ...
4
votes
1answer
206 views

Why curl of Dirac string attached to Dirac monopole is zero?

So let we have a magnetic field which is $$B_\mu=\frac{q}{2}\frac{x_\mu}{|x|^3}-2\pi q\delta_{3\mu}\theta(x_3)\delta{(x_1)}\delta{(x_2)},\tag{4.65}$$ where $\theta$ is step function and $\delta{(x_\mu)...
2
votes
2answers
141 views

Does introducing a gauge field into the complex scalar field theory Lagrangian change its dynamics?

I've been reading Lancaster & Blundell, and in Chapter 14 they focus on the Lagrangian $$ \mathcal{L}=(\partial^\mu\psi)^\dagger(\partial_\mu\psi) - m^2\psi^\dagger\psi. $$ To impose invariance to ...
3
votes
1answer
85 views

Most general Gauge Lie group in a Yang-Mills theory

Mathematicians have done a complete classification of all possible Lie groups. Is there a set of conditions that allows us to identify which Lie groups from the classification can possibly act as a ...
1
vote
1answer
76 views

Is there any (locally) conserved charges associated to gauge symmetries?

I'm currently in my second year of master. From what I understand, in QFT, Noether's first theorem implies that for any continuous symmetry (i.e. associated to a $n$-dimensional Lie group $G$, $n\geq ...
0
votes
1answer
169 views

What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?

In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for. Flip Tanedo (a ...
3
votes
1answer
125 views

Does one ever need infinitely many cohomologies?

In a theory containing gauge fields or higher-form gauge fields, if the background spacetime is a complicated manifold, a nice way to represent the configuration of the gauge field mathematically is ...
1
vote
0answers
57 views

Maxwell solution in differential forms

Maxwell equation's in differential form: $dE = 0 \ and\ \ (\ast d \ast)E = p$ in static situation. Where $E \in \Omega^1(U)$, $p \in \Omega^0(U)$, $\ast$ is hodge star operator, $U= \mathbb{R}^3$ ...

1 2
3
4 5
34