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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14 views

Infinitesimal gauge invariance of Yang--Mills Lagrangian

Under an infinitesimal gauge transformation $g(x) = 1 - i\alpha{}_i(x)T{}^i$, where $[T{}^a, T{}^b] = if{}^{ab}{}_c T{}^c$, I want to know what happens to the Lagrangian $\mathcal{L} = ...
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41 views

Magnetic monopoles gauge theories

I'm quoting 't Hooft: "[...] Locally stable field configurations may exist that have some topological twist in them [...].Careful analysis of the existing Lie groups and the way they may be ...
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1answer
58 views

Particle on $S^1$ and $U(1)$-principal bundle

I have a question arisen from a simple QM problem: let consider a boson on $S^1$ minimally coupled with a constant gauge field $A$. Taking the stationary Schrödinger (S) or Klein-Gordon (KG) equation ...
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1answer
54 views

Unphysical degrees of freedom in the Yang Mills Lagrangian [duplicate]

Im taking my first course in QFT and has stumbled upon something that I do not understand. Given the Yang Mills lagrangian $$\mathcal{L} = -\frac{1}{4}F^{a}_{\mu \nu}F^{a\mu \nu}$$ with $F^{\mu ...
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1answer
46 views

Left-right topology

Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking \begin{equation} SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to ...
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294 views

Why can't a real scalar couple to the electromagnetic field?

If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ ...
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1answer
66 views

Is the standard model a quantized gauge theory?

I have studied some quantum field theory and gauge theory but I am definitely not an expert. I am aware that in quantizing electrodynamics one has to fix a gauge. I have read that for general gauge ...
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15 views

how to construct a model with fully broken SU(2) gauge symmetry, in which the masses of all three vector bosons are different

When we do the spontaneous symmetry breaking of SU(2) local gauge symmetry, the three vector fields acquire mass which is equal for all three of them. Now how do I construct a model in which the ...
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2answers
43 views

Do Weyl fermions carry electric charge?

Do Weyl fermions carry ordinary electric charge? That is, do they interact with, for instance, electrons or photons?
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25 views

Simplify $K$-matrix

2+1D Abelian topologically ordered states are believed to be described by multicomponent $U(1)$ Chern-Simons theories, with Lagrangian \begin{equation} ...
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1answer
48 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
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41 views

Explicit derivative of Chern-Simons current

I know that for a Chern-Simons 3-form $\omega=\operatorname{Tr}\left[F\wedge A-\frac{1}{3}A\wedge A\wedge A\right]$, with $F=A\wedge A +\operatorname{d}A$, I should get ...
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14 views

On the action of superconformal generators in maximally supersymmetric Yang-Mills

Consider maximally supersymmetric Yang-Mills theory in 3+1 dimensions. This theory has 32 supercharges: 16 ordinary ones, conventionally labeled $Q$; and 16 superconformal ones, conventionally ...
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2answers
117 views

Scalar and Vector Potential

I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, ...
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0answers
26 views

Gauge mediated SUSY breaking

I have seen it claimed that in SUSY gauge mediated breaking there can be no flavour changing terms because the mediation is flavour blind. What does this mean and how does it work?
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1answer
46 views

What is the importance of vector potential not being unique?

For a magnetic field we can have different solutions of its vector potential. What is the physical aspect of this fact? I mean, why the nature allows us not to have an unique vector potential of a ...
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1answer
119 views

Why are string theorist so indifferent to the gauge structure of gravity? [closed]

Gravity shares many of the characteristics of Yang-Mills gauge theory. For example, the affine connection plays the similar role as the gauge potential in gauge theory, the Riemann tensor plays the ...
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0answers
49 views

Non-null hessian condition for regular dynamical systems

I'm "researching" on unquantised Yang-Mills theory. For that I'm studying the Dirac's method for singular constrained systems and having problems to follow the first considerations on that matter. I ...
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1answer
113 views

What is the relationship between BRST symmetry and gauge symmetry?

As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following: "when QFT was reformulated in fiber bundle language for application to ...
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0answers
33 views

What's the relation between representation theory and mass / electric charge?

This is a follow-up on this answer, where ACuriousMind wrote Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, ...
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1answer
22 views

Gauge transformation of wave function of a system of stationary charges

Let's say we have a system of $n$ stationary charges interacting via Coulomb potential. Let's ignore possible external electromagnetic fields. Moreover the system is quantum, and its wave function is ...
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1answer
66 views

Why do different vector potentials in Landau levels problem lead to different quantum mechanical ground state wavefunctions?

Consider a charged particle (electron) moves in xy plane under a magnetic field pointing along the z direction, i.e., $\vec{B}=B\hat{z}$. As a consequence, we can write down three different gauges- ...
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1answer
215 views

Why is there no fundamental force following from the $SU(4)$ symmetry?

I've understood that the three fundamental interactions described by the Standard Model (the electromagnetic, the weak and the strong force) are thought to correspond (roughly) to gauge invariances ...
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1answer
43 views

What is the meaning of 'physical gauge'?

What does it mean for a gauge to be a physical gauge in your gauge choice of the theory, and why is it called the "physical gauge"?
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1answer
48 views

Derivation Of The Equation Of Motion Of String from Polyakov action

I'm stuck at a step in the derivation of the equations of motions of a string using the Polyakov action. In Polchinski's textbook in String Theory , Page 14 ; Equation ( 1.2.25 ) , Varying the ...
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1answer
101 views

Hamiltonian and Energy of a charged particle in an Electromagnetic field

The Lagrangian of a charged particle of charge $e$ moving in an electromagnetic field is given by $$L=\frac{1}{2}m\dot{\textbf{r}}^2-e\phi-e\textbf{A}\cdot \textbf{v}$$ where $\phi(\textbf{r},t)$ is ...
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1answer
35 views

Coupling constant in the Yang-Mills action

Intuitively, gauge coupling defines the strength of interactions between fields. But how to interpret the coupling $1/g^2$ in front of the kinetic term of Yang-Mills theories, ...
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1answer
73 views

Some questions about gauge theory

Let's talk quantum mechanics. I have a charged particle moving on a sphere. It has a wave function $\psi$. At time $t=0$, there is no magnetic flux piercing the sphere. Instantaneously, I introduce a ...
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3answers
86 views

Gauge invariance in classical electrodynamics

I think that I don't fully understand concept of gauge invariance. Suppose we have a Lagrangian for classical ED which is: $$\mathcal{L} = -\frac{1}{4} (F_{\mu \nu})^2 - j^{\mu}A_{\mu}.$$ First part ...
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37 views

Gravity as a gauge theory - Cartan-Killing form?

First, let me state the form of Lagrangian for YM and GR \begin{align} L_{YM} = \alpha \textrm{tr}(F^2), \qquad L_{GR} = \beta R \end{align} I heard, YM is a gauge theory but GR isn't a really gauge ...
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1answer
33 views

What is the relation between interaction range and the mass of gauge bosons?

I have just started to read spontaneous symmetry breaking, where it is mentioned that EM fields are infinite in range, so the gauge boson has to be massless, while for the strong and weak ...
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1answer
45 views

Which groups can be lattice gauge groups?

Let me state first off that in this question I am most interested in lattice gauge theories, and not necessarily with Fermion couplings. But if Fermions and continuum gauge theories can also be ...
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2answers
70 views

Wave function constrained to a fixed trajectory? Really?

this is probably a very stupid question. First of all, I'm a mathematician so please try to use coordinate-free notations. It's often used in quantum mechanics a wave function depending on a fixed ...
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1answer
55 views

Supertrace of holonomy of commutator

On page 47 of Surface operators in four-dimensional topological gauge theory and Langlands duality by Kapustin et al., the following expression is given \begin{equation} ...
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0answers
47 views

Coordinate variation of a Wilson loop

In Chern Simons Gauge Theory as a String Theory, Witten derives the general coordinate variation of a Wilson loop, i.e., equation 3.11. My question is, how does one derive this? I only managed to ...
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0answers
51 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?
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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 ...
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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 ...
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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, ...
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1answer
55 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 ...
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1answer
79 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
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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 ...
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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 ...
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1answer
68 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 ...
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 ...
4
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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 ...
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2answers
121 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
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
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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
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1answer
91 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 ...