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2
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1answer
68 views

Are the Yang-Mills equation and its generalization gauge invariant?

I have derived the Yang-Mills equation and its generalization coupled to a current of a scalar field $\phi$ by extremalizing the action describing a $\mathrm{SU}(2)$ scalar field gauge theory: ...
2
votes
1answer
81 views

Railguns and Gauge Invariance

Paul J. Cote and Mark A. Johnson of Benet Laboratories, Army Research, Engineering and Development Command wrote a series of short papers on the vector potential arising from their attempts to solve ...
4
votes
1answer
64 views

Only transverse photons are gauge-invariant (Peskin page 298)

Seven lines down from the top of page 298 of P & S, it says "Single particle states containing one electron, one positron, or one transversely polarized photon are gauge-invariant, while states ...
1
vote
2answers
76 views

What is the reason for the $ i \tau_2 $ - factor in the higgs coupling with up-type quarks?

The quark mass term in the Standard Model Lagrangian looks like this: $$ L = - \lambda_d \bar{Q}\phi d_R - \lambda_u \bar{Q} i \tau_2 \phi^* u_R $$ What is the reason for the $ i \tau_2 $ - ...
2
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0answers
24 views

Massive photon and gauge invariance of S-matrix amplitude

Let's have minimally extended gauge invariant lagrangian (with free kinetic term of EM field): $$ \tag 1 L (\Psi , \partial_{\mu} \Psi) \to L (\Psi , D_{\mu}\Psi ) - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}, ...
2
votes
0answers
40 views

Momentum operator of a particle in an electromagnetic field

In quantum mechanics, to all observables correspond some self-adjoint operators. In the absence of an electromagnetic field the momentum operator is clearly $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
4
votes
1answer
106 views

Is gauge connection unique?

In QFT, given a gauge group and matter field, is the form of the gauge field unique? In other words, given a principal G-bundle and its associated vector bundle, is the construction of the principle ...
2
votes
1answer
101 views

Mass term in the Lagrangian

I have read that the mass term appearing in the electroweak Lagrangian stops it (the Lagrangian) from becoming gauge invariance. Can someone explain where and why this term is creating the problem?
1
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0answers
34 views

The Ward identity for EM amplitude with massive vector boson

Let's have theory of massive vector boson interacting with EM field: $$ L = |D_{\mu}W_{\nu} - D_{\nu}W_{\mu}|^{2} + m^{2}|W|^{2}, \quad D_{\mu} = \partial_{\mu} - ieA_{\mu}. $$ The question: how to ...
4
votes
0answers
98 views

Gauge Invariance of Yang Mills Lagrangian

I am trying to show the invariance of the following Yang Mills Lagrangian: $$L= -\frac{1}{4} F^a_{\mu \nu} F_a^{\mu\nu} + J_a^\mu A_\mu^a$$ under the following gauge transformation ($\theta$ being a ...
5
votes
0answers
83 views

Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
3
votes
2answers
124 views

When can we add a total time derivative of $f(q, \dot{q}, t)$ to a Lagrangian?

The other day, I was listening to this lecture on the Lagrangian for a charged particle in an electromagnetic field, and at one point in the video, the lecturer mentions that we can add any total time ...
2
votes
2answers
73 views

Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies Gauge redundancy for 1-forms,'photons'. Does this argument go through to p-forms? That is does lorentz invariance of s-matrix of ...
2
votes
1answer
112 views

Conjugate momentum is not gauge invariant

The conjugate momentum of a charged particle moving in a uniform magnetic field is given by $$\vec p=m\vec v+q \vec A$$ This expression is not unique because $\vec A$ is not unique. $\vec A$ is not ...
6
votes
1answer
176 views

Why does local gauge invariance suggest renormalizability?

I'm reading Gauge Field Theories: An Introduction with Applications by Mike Guidry and this particular remark is not obvious to me: A tempting avenue is suggested by the QED paradigm, for if a ...
2
votes
1answer
41 views

A single valued function from a multi-valued function

In Schrieffer's book "Theory of Superconductivity", there is said when he deals with multiple connected superconductors (and discuss London equations), that if one takes the line integral of the ...
4
votes
1answer
91 views

$U(1){\times}U(1)$ local gauge invariance derivative

In QED and the basic Higgs mechanism, there is a local gauge transformation where a scalar field $\phi$ is transformed as: $e^{i\theta\eta(x)} \phi$ The partial derivative of this however makes the ...
3
votes
1answer
103 views

Is obtaining the coordinate representation of momentum operator from commutator more fundamental than generator of translation

Related post: What is the most general expression for the coordinate representation of momentum operator? There are two methods of obtaining the coordinate representation of momentum in quantum ...
7
votes
1answer
75 views

Connection beween infinite gauge symmetries and UV finiteness

In e.g., http://arxiv.org/abs/arXiv:0712.3526 the author claims: Since the massless higher-spin field theories involve infinite-dimensional gauge symmetries, one expects that such theories may be ...
6
votes
2answers
199 views

The gauge covariant derivative and it's substitution

I was wondering wether it would make a difference (in general) if I were to were introduce the gauge covariant derivative $$D_\mu=\partial_\mu+ieA_\mu$$ In the Lagrangian density and then derive the ...
3
votes
1answer
143 views

What are type system examples of local gauge transformation- and field strength-like objects?

This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types. A field $$\psi:\mathcal M\to\mathbb C^n$$ is a section of the ...
2
votes
1answer
97 views

Why gauge invariance for electromagnetic fields?

What is the physical constraint that gauge invariance is a required condition for electromagnetic fields? What would happen if the electromagnetic fields were not gauge invariant?
0
votes
1answer
47 views

How to deal with $\vec{j}\cdot\vec{A}$ or $\rho A^2$ interaction when utilizing Kubo formula? Gauge invariance?

If there exist electromagnetic fields in solids, electrons can feel interactions like $\vec{j} \cdot \vec{A}$ or $\rho A^2$ (these are not regarded as perturbations). But these are not gauge ...
0
votes
1answer
214 views

Integrating the gauge covariant derivative by parts

I was watching a set of lectures on effective field theory and the lecturer said that you can always integrate the covariant derivative by parts due to gauge symmetry. For example, if I understand ...
6
votes
1answer
154 views

What do people mean by gauge invariance of the normalization of field?

Lets have the scalar Klein-Gordon field interacting with EM field: $$ L = \partial_{\mu}\varphi \partial^{\mu}\varphi - m^2\varphi \varphi^{*} - j_{\mu}A^{\mu} + q^{2} A_{\mu}A^{\mu}\varphi ...
4
votes
1answer
204 views

Field strength vanishes iff $A_{\mu}$ is pure gauge

Is it true that the field strength $F_{\mu\nu}$ in a non-Abelian gauge theory with gauge group $G$ vanishes if, and only if, the gauge field $A_{\mu}$ is a pure gauge? I can show one implication. ...
1
vote
1answer
128 views

Global SU(2) invariance of QED Lagrangian

I'm having problems seeing the global SU(2) invariance of the QED Lagrangian. My specific problem is seeing why \begin{equation} e^{-i a_i \sigma_i} \gamma_\mu e^{i a_i \sigma_i} = \gamma_\mu ...
11
votes
1answer
265 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 ...
5
votes
1answer
323 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
5
votes
0answers
155 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
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 ...
0
votes
0answers
83 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 ...
4
votes
2answers
209 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.
2
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0answers
112 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
212 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
310 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
102 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 ...
5
votes
1answer
181 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 ...
8
votes
0answers
154 views

Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- ``Gauge fields and strings''. Action for the ...
1
vote
1answer
160 views

Different invariant gauge groups (IGG) on different lattices with the same form mean-filed Hamiltonian?

Suppose that we use the Schwinger-fermion ($\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$) mean-field theory to study the Heisenberg model on 2D lattices, and now we arrive at the mean-field ...
4
votes
3answers
364 views

Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum] Note that we may morally include general relativity in the gauge theories. We may have several (some are deliberately ...
0
votes
1answer
148 views

How to verify gauge invariance of an amplitude

I have calculated a tree level amplitude for Compton scattering (${e\left(p\right)+\gamma\left(k\right)\to e\left(p\prime\right)+\gamma\left(k\prime\right)}$): $${ ...
1
vote
1answer
280 views

Local gauge invariance and fields

I have one question about local gauge invariance of the spinor and scalar theories. For the scalar complex field with lagrangian $L_{0}$ requirement of local gauge invariance leads us to the ...
1
vote
2answers
293 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 ...
4
votes
1answer
281 views

Is reparameterization invariance some kind of gauge symmetry?

On page 116 of this book it is said, that reparameterization invariance of the string action is analogous to the gauge invariance in electrodynamices. Whereas Maxwell's equations are symmetric under ...
2
votes
1answer
1k views

Lorenz and Coulomb gauge-fixing conditions

Lorenz and Coulomb gauge-fixing conditions. What is physical difference between these two gauge-fixing conditions? Mathematical expression are clear but how to we choose one of these means what they ...
3
votes
1answer
307 views

How to introduce the electromagnetic field in Quantum Field Theory?

There are many ways to introduce the electromagnrtic field in Quantum Field Theory(QFT), such as canonical quantization method which introduces the creation and annihilation oprators by treating the ...
2
votes
2answers
165 views

A question for the generalization of gauge transformation with two antisymmetric indices

I have a question about the generalization of gauge transformation with two antisymmetric indices. Starting from Eq. (3.7.6) in Polchinski's string theory book p. 108. $$S_{\sigma} = \frac{1}{4 \pi ...
4
votes
3answers
352 views

Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...
9
votes
1answer
262 views

Invariance of Functional Integration Measure

Let us consider the functional integral: \begin{equation} \int \mathcal{D} A e^{iS[A]} \end{equation} where $S[A]$ is the action for $U(1)$ gauge field and \begin{equation} \mathcal{D}A\equiv ...