The gauge-theory tag has no wiki summary.
2
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1answer
175 views
Large gauge transformations
I would like to understand what is the importance of large gauge transformations. I read that these gauge transformation cannot be deformed to the identity, but why should we care about that?
4
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2answers
264 views
Gauge fixing and equations of motion
Consider an action that is gauge invariant. Do we obtain the same information from the following:
Find the equations of motion, and then fix the gauge?
Fix the gauge in the action, and then find the ...
3
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1answer
98 views
Weak isospin confinement?
According to the Wikipedia article on color confinement:
The current theory is that confinement is due to the force-carrying gluons having color charge [...],
i.e. because the gauge group is ...
1
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1answer
59 views
How is $ g^2 N$ held fixed in the large N limit?
In 't Hooft's original paper:
http://igitur-archive.library.uu.nl/phys/2005-0622-152933/14055.pdf
he takes $N \rightarrow \infty $ while $ g^2 N$ is held fixed. Is this just a toy model? Or is there ...
2
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3answers
129 views
Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?
An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
3
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1answer
256 views
Gauss law in classical U(1) gauge theory
I can see that $a_{0}$ is not an independent field and Gauss law is a constraint on the theory arising from field equations. But, I don't get the geometrical picture.
Let $A$ be the space of all ...
2
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0answers
92 views
Pseudo scalar mass and Pure scalar mass
Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact?
For ...
4
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2answers
267 views
Intuition for gauge parallel transport (Wilson loops)
I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport".
I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
2
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1answer
144 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
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2answers
93 views
What exactly is the weak portion of the SM gauge group?
This Wikipedia article: http://en.wikipedia.org/wiki/Left%E2%80%93right_symmetry states that the weak part of the SM gauge group is not $SU(2)_L \times U(1)_Y$ but $ \frac{ SU(2)_L \times ...
2
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2answers
216 views
Counting degrees of freedom in presence of constraints
In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
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4answers
401 views
First class and second class constraints
Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
3
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1answer
152 views
Does spontanous symmetry breaking affect Noethers theorem?
Does spontanous symmetry breaking affect the existence of a conserved charge?
And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)?
...
2
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0answers
109 views
Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius
Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
2
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1answer
210 views
Wilson loops and gauge invariant operators (Part 2)
These questions are sort of a continuation of this previous question.
I would like to know of the proof/reference to the fact that in a pure gauge theory Wilson loops are all the possible gauge ...
5
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3answers
359 views
Gauge fixing choice for the gauge field $A_0$
In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole.
Please can you provide me a ...
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2answers
124 views
Is the Chern-Simons integral of gauge fields over black hole singularities zero?
Suppose we have an evaporating black hole and a nonabelian Yang-Mills theory with a $\theta$ topological term. This counts the total number of instantons minus antiinstantons. Consider the total ...
2
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1answer
261 views
Wilson loops and gauge invariant operators (Part 1)
I guess the Hilbert space of the theory is precisely the space of all gauge invariant operators (mod equations of motion..as pointed out in the answers)
Is it possible that in a gauge theory the ...
5
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1answer
305 views
Taking the continuum limit of $U(N)$ gauge theories
I would like to draw your attention to appendix $C$ on page 38 of this paper.
The equation $C.2$ there seems to be evaluating the sum $\sum_R \chi _R (U^m)$ in equation 3.16 of this paper. I ...
2
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1answer
125 views
Is there any good gauge-fixing prescription for discrete gauge symmetries?
Nearly all gauge-fixing prescriptions are based upon setting some function involving the gauge fields to be zero. That function is continuous and varies over the real/complex numbers. Trying the same ...
5
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2answers
150 views
Are timelike diffeomorphisms really redundancies in description in quantum gravity?
Are timelike diffeomorphisms really redundancies in description in quantum gravity? Certainly Yang-Mills gauge transformations can be considered redundancies in description. Ditto for p-form ...
2
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1answer
68 views
How do we deal with Gribov ambiguities when calculating in quantum gauge theories?
How do we deal with Gribov ambiguities when actually calculating in quantum gauge theories? Any literature references?
3
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1answer
178 views
Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles
I am reading this research paper authored by NS Manton on the Force between 't Hooft-Polyakov monopoles. I have a doubt in equation 3.6 and 3.7. We assume the gauge field for a slowly accelerating ...
3
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1answer
318 views
Noether current for the Yang-mills-higgs lagrangian
I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
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0answers
46 views
Limit of the scalar field, and potential for a soliton ( finite energy, non dissipative) solution
I want to prove that the the scalar field of the yang-mills lagrangian tends to some constant value which is a function of theta at infinity and that this value is a zero of the potential, when we ...
5
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3answers
246 views
Could general relativity and gauge theories in principle be covered in one course?
It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the ...
3
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2answers
404 views
What is the ontological status of Faddeev Popov ghosts?
We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
1
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1answer
172 views
What is the winding number of a magnetic monopole, and why is it conserved
I had asked a similar question about a calculation involving the winding number here. But i haven't got a satisfactory response. So, I am rephrasing this question in a slightly different manner. What ...
3
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2answers
189 views
Counting degrees of freedom of gauge bosons
Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization ...
1
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1answer
238 views
Why are all observable gauge theories not vector-like?
Why are all observable gauge theories not vector-like?
Will this imply that the electron and/or fermions do not have mass?
How is this issue resolved?
Background:
The Standard Model is a ...
5
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2answers
322 views
Winding number in the topology of magnetic monopoles
I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
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0answers
75 views
How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer?
How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer? There are some gauges with negative norms. It's true that if restricted to gauge invariant states, the ...
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241 views
The meaning of Goldstone boson equivalence theorem
The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
4
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1answer
156 views
Gauge symmetry description for $\phi^4$?
That is a follow-up to this question: Gauge symmetry is not a symmetry?
Ok, gauge symmetry is not a symmetry, but ...
... a redundancy in our description, by introducing fake degrees of freedom ...
2
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2answers
180 views
What evidence is there for the electroweak higgs mechanism?
The wikipedia article on the Higgs mechanism states that there is overwhelming evidence for the electroweak higgs mechanism, but doesn't then back this up. What evidence is there?
5
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0answers
156 views
Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?
The compact U(1) lattice gauge theory is described by the action
$$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$
where the gauge connection $A_l\in$U(1) is defined ...
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0answers
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How to determine if an emergent gauge theory is deconfined or not?
2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
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1answer
487 views
Yukawa Coupling of a Scalar $SU(2)$ Triplet to a Left-Handed Fermionic $SU(2)$ Doublet
Suppose we have a field theory with a single complex scalar field $\phi$ and a single Dirac Fermion $\psi$, both massless. Let us write $\psi _L=\frac{1}{2}(1-\gamma ^5)\psi$. Then, the Yukawa ...
3
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2answers
327 views
The Faddeev-Popov Lagrangian
This is a non-abelian continuation of this QED question.
The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by
$$
...
6
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4answers
589 views
What's the distinctions between Yang-Mills theory and QCD?
So Yang-Mills theory is a non-abelian gauge theory, and we used a lot in QCD calculation.
But what are the distinctions between Yang-Mills theory and QCD?
And distinctions between supersymmetric ...
3
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1answer
248 views
QED BRST Symmetry
This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim:
"Consider QED ...
2
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1answer
22 views
Time Evolution of a Manifold Embedding
Given a smooth manifold $\mathcal{M}$ with a simplicial complex embedding $\mathsf{S}$, what specific tools or methods can be used to give an analysis of the time evolution of the manifold given some ...
5
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2answers
269 views
Why do we like gauge potentials so much?
Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
2
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2answers
74 views
Gauge invariant scalar potentials
If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
4
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1answer
184 views
Gauge invariance and the form of the Rarita-Schwinger action
in Weinberg Vol. I section 5.9 (in particular p. 251 and surrounding discussion), it is explained that the smallest-dimension field operator for a massless particle of spin-1 takes the form of a field ...
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2answers
216 views
Can an Electromagnetic Gauge Transformation be Imaginary?
The Hamiltonian of a non-relativistic charged particle in a magnetic field is
$$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$.
Under a gauge transformation ...
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Attempts to explain Higgs coupling as a gauge transformation symmetry
As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant ...
3
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2answers
415 views
How does non-Abelian gauge symmetry imply the quantization of the corresponding charges?
I read an unjustified treatment in a book, saying that in QED charge an not quantized by the gauge symmetry principle (which totally clear for me: Q the generator of $U(1)$ can be anything in ...
3
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1answer
177 views
SU(2) yang-mills EOM
I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor
$$ ...
5
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1answer
212 views
Can a photon see ghosts?
Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories?
Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
