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. ...

learn more… | top users | synonyms

1
vote
1answer
44 views

D7 brane profile

I have a doubt about the differential equation leading to the profile of a d7 brane embedded in a 10 dimensional space. According to http://arxiv.org/abs/hep-th/0306018, equation (6), we have the ...
3
votes
1answer
158 views

Fundamental representation in quantum field theory

In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the ...
1
vote
2answers
71 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 $ - ...
1
vote
1answer
44 views

Why does the state space contain states with negative norm and what would be an example?

My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?
2
votes
1answer
56 views

Scalar Particles, Flavor Changing Processes and Gauge Symmetries

Let's consider an extended version of the Standard Model (SM) with a new Yukawa operator of the form $$ \sum_\ell g_\ell\bar{\ell}\ell \phi ,$$ where $\ell$ is any lepton of the SM and $\phi$ is a new ...
4
votes
1answer
44 views

No local degrees of freedom when connection is flat

I was studying Chern-Simons theory and variation of action gives us the flatness conditions $\mathrm{d} A + A \wedge A = 0$. I am wondering how to see that this implies there are no local degrees of ...
0
votes
0answers
39 views

Using local U(1) Transformation to solve Problem in Path Integral [duplicate]

When we develop photon path integral, we assume that the current is always conserved. But if we consider interaction between electron/positron and photon, the Noether current is conserved only when ...
2
votes
2answers
70 views

Independent components in a 4-vector representing massless fields

In Ryder Page141, it is written "the electromagnetic field, like any massless field, possesses only two independent components, but is covariantly described by a 4-vector $A_{\mu}$". Why are there ...
0
votes
1answer
78 views

General relativity: gauge fixing

In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...
1
vote
0answers
30 views

Equations of motion with replacing the Lagrangian by irrep diagrams generating functional

I have read that equations of motion of ghosts is equal to $$ \tag 1 \frac{\delta \Gamma}{\delta \bar{c}^{a}(x)} = -\partial^{\mu}_{x}\frac{\delta \Gamma}{\delta K^{\mu , a}(x)}, $$ where $\Gamma = W ...
2
votes
0answers
35 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 $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
3
votes
0answers
37 views

How the number of charges (colors) and the number of photons (gluons) is connected?

This question is a continuation of "Can a third type of electrical charge exist?" and specifically this comment. I know the common knowledge that there is 1 kind of electric charge and thus 1 kind of ...
6
votes
1answer
108 views

Variational derivatives of strongly connected diagrams functional in gauge theory

Background In Jorge C. Romao's "Advanced Quantum Field Theory", at the end of page 218, Eq (6.266) reads: $$\tag{1} \left.\frac{\delta^{2}}{\delta \omega^{b}(y)\delta A_{\mu}^{c}(z)}\left[ ...
4
votes
0answers
63 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
4
votes
0answers
49 views

Chern-Simons on a lattice and the framing anomaly

Can someone make or refer me to the argument for why $U(1)$ Chern-Simons theory in three dimensions cannot be defined by a lattice action? (Unlike Dijkgraaf-Witten theories, which are defined on the ...
0
votes
0answers
16 views

What potential between charges leads to confinement

In (2+1)-d, instanton effect leads to a linear potential between charges. If we have two particles with opposite charges in this case, since linear potential diverges when the distance between the two ...
0
votes
0answers
18 views

Unitary gauge in $Z_2$ lattice gauge theory with matter field

A $Z_2$ gauge theory with Ising matter field on a 2-dimensional square lattice has the Hamiltonian \begin{equation} H=-t\sum_{\vec r,j}\sigma_j^x(\vec r)-g\sum_{\vec r}\sigma^z_1(\vec ...
3
votes
0answers
57 views

Getting Slavnov-Taylor identity

Let's have generating functional in path integral form for gauge $SU(n)$ theory with interaction: $$ \tag 1 Z[J] = \int DB D\bar{\Psi}D\Psi D\bar{c}Dc e^{iS}. $$ Here $$ S = S_{YM}(B, \partial B) + ...
2
votes
0answers
31 views

Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
4
votes
1answer
101 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 ...
3
votes
1answer
94 views

Is there a method which quantizes non-abelian gauge theories without path integrals formalism?

In the most QFT books there is a method of quantization of non-abelian theories through path integral methods. But I want to learn also the other methods without using of this formalism. Does anyone ...
7
votes
1answer
203 views

Gauge Field Tensor from Wilson Loop

It is possible to introduce the gauge field in a QFT purely on geometric arguments. For simplicity, consider QED, only starting with fermions, and seeing how the gauge field naturally emerges. The ...
5
votes
2answers
143 views

Questions about the degree of freedom in General Relatity

I'm confused about the number of degrees of freedom in General Relatity. There are two ways to count it. However, they are contradictory. For simplicity, we consider vacuum solution. First, ...
3
votes
2answers
83 views

Utility of gauge four-potential $A_{\mu}$ (as opposed to electric and magnetic fields ${\bf E}$ and ${\bf B}$) in E&M?

The action for an electromagnetic field with source charges is given by $$S= \int \left\{ \frac{1}{4\mu_0}F^{\mu\nu}F_{\mu\nu} - J^\mu A_\mu \right\}dx$$ By setting $dS=0$ and taking the Lorenz ...
6
votes
2answers
322 views

Faddeev-Popov Ghosts

When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field ...
0
votes
0answers
35 views

U(1) local gauge transformation for Dirac spinor field

How can we define U(1) local gauge transformation for Dirac spinor field?, like scalar fields?
3
votes
1answer
40 views

How do we know what type of gauge field to add to a theory?

I've been watching Leonard Susskind's particle physics lectures and in one lecture, he discusses a very simple gauge theory. We have a complex scalar field $\phi(x)$ with Lagrangian $$\mathscr{L} = ...
4
votes
1answer
77 views

Why do we need to prove the gauge invariance of QED (or all of the gauge theories) on the Feynman diagrams language?

Let's have the QED lagrangian. It has explicit gauge invariance, so, by the naive thinking, all of the EM processes must satisfy the property of gauge invariance. So why do we need to recheck of gauge ...
4
votes
2answers
98 views

Why are the “coupling constants” constant?

The coupling constants (in the gauge theory) fix an inner product on the lie algebra of the gauge group and we use it to define strength of the fields. we are using ad-invariant inner products which ...
1
vote
0answers
35 views

compact and non-compact gauge theory [closed]

From the answer to this question, I see that the gauge theory has to be compact if the charges need to be quantized. I am not sure in what sense these are necessary and sufficient. So here is a ...
1
vote
1answer
101 views

What exactly is a gauge anomaly?

In lots of papers I read about gauge anomalies. For example, avoiding gauge anamolies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anamolies in the Standard Model are ...
4
votes
3answers
232 views

What is the basis of gauge theory?

I’m learning about gauge concepts. I’ve always had the idea that by looking at a phenomenon from different viewpoints, that symmetries could be derived – in fact, that was what an equal sign ...
1
vote
1answer
69 views

Has a metric formulation of electromagnetism ever been attempted? [duplicate]

I understand that electromagnetic fields carry energy, and this energy curves spacetime gravitationally. That's not my question. I'm asking if anyone has tried to formulate electromagnetism in such ...
1
vote
3answers
78 views

About constraints of the first class and electrodynamics

Let's have some theory in hamilton formalism and let's assume that it has the constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx ...
3
votes
0answers
73 views

Naive questions on the classical equations of motion from the Chern-Simons Lagrangian

Consider a Chern-Simons Lagrangian $\mathscr{L}=\mathbf{e}^2-b^2+g\epsilon^{\mu \nu \lambda} a_\mu\partial _\nu a_\lambda$ in 2+1 dimensions, where the 'electromagnetic' fields are $e_i=\partial ...
5
votes
3answers
160 views

Global vs. local gauge group in mathematical sense - physics examples?

Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group: Local gauge group $G$. Corresponds to the fibers of the ...
3
votes
1answer
74 views

Yang-Mills Lagrangian invariant under BRST

In equation 16.47 in Peskin & Schroeder, it is claimed that $$ -\frac{1}{2}g^2f^{abc}f^{cde}\left(A_{\mu}\,^{b}c^{d}c^{e}+A_{\mu}\,^{d}c^{e}c^{b}+A_{\mu}\,^{e}c^{b}c^{d}\right) ~=~ 0 \tag{16.47}$$ ...
6
votes
1answer
192 views

History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, but could you explain the history? It's ...
4
votes
1answer
80 views

The 6-j symbol and intersecting Wilson loops, redux

This is a quite specific question continuing the problems I have with computing the expectation value of intersecting Wilson loops I laid out here. Using the tools from the answer there, I quite ...
5
votes
0answers
77 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. ...
8
votes
2answers
127 views

Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
6
votes
1answer
138 views

Intersecting Wilson loops in 2D Yang-Mills

I am currently trying to understand 2D Yang-Mills theory, and I cannot seem to find an explanation for calculation of the expectation value of intersecting Wilson loops. In his On Quantum Gauge ...
8
votes
2answers
134 views

Why gauge $SU(N)$ and not $SO(N)$?

When building models people typically gauge $SU(N)$ but rarely try to gauge $SO(N)$ (the only example I know about is $SO(10)$, but even that isn't quite $SO(10)$ but actually its double cover). At ...
6
votes
1answer
53 views

How many coupling constants if my gauge group has many factors?

I am reading a review article where $U(1)\times{}SU(2)\times{}SU(3)$ gauge transformations are considered. It says that when such a gauge transformation is done the gauge fields $A^{\alpha}_{\mu}$ ...
4
votes
0answers
61 views

Why does strong interaction increase with distance?

I read numerous times that strong interaction increases with distance. But how can one actually derive the force-distance relation from the lagrangian (quark field + gluon field + gauge coupling)? ...
1
vote
1answer
109 views

A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
2
votes
2answers
72 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 ...
5
votes
3answers
304 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
2
votes
1answer
129 views

Equations of motion for the Yang-Mills $SU(2)$ theory

I have an exercise for Yang-Mills theory. I can't find answer anywhere. Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar ...
1
vote
0answers
17 views

Lattice Gauge and Spin Network

I see the similarity between the Lattice Gauge and Spin Network . (For example , the both theories depict the node part as quantum (the latter is explained as spin)) Are there any other ...