All Questions
Tagged with wilson-line or wilson-loop
126 questions
4
votes
2
answers
134
views
How to make sense of non-planar Wilson loops on the lattice?
I am operating with a (more or less standard) Metropolis+Overrelaxation algorithm a series of Wilson loops on a $N_t\times N_s^2=48^2\times 16$ (2+1) dimensional Euclidean lattice. I am simulating ...
- 302
8
votes
0
answers
132
views
Wilson lines and Bremsstrahlung in Quantum Electrodynamics
Short: How can I use Wilson lines to compute Bremsstrahlung? I'm particularly interested in QED, as a simple example.
Long:
I recently learned what is a Wilson line, in the simplest sense of
$$W[C] = ...
- 25.7k
3
votes
1
answer
151
views
The Wilson loop [duplicate]
In Peskin's QFT page 492 (section 15.3). I faced the calculation of Wilson loop which is
And the writer says it is equal to
I understood that field strength tensor can be written as curl of ...
- 101
1
vote
0
answers
103
views
Dirac quantization condition of chern-simons theory on a open manifold
Let us consider an abelian Chern-Simons theory on a disk with compactified time direction:
$$S=\frac{iN}{2\pi}\int_{\mathbb{D}^2\times \mathbb{S}^1}AdA.$$
For simplicity I have set $N\in \mathbb{Z}$ ...
- 179
2
votes
1
answer
203
views
Gauge transformation of Wilson line
This question is prompted by Exercise 25.6 of Schwartz's Quantum Field Theory and the Standard Model. The first part of the exercise asks you to show that the path-ordering in the definition of a ...
- 83
0
votes
0
answers
68
views
Why is there a phase shift in the Wilson loop?
Calculating the $\theta$-vacuum expectation $\langle \theta | W (C) | \theta \rangle$ of the Wilson loop operator $W (C)$ is equivalent to evaluating the energy of two charges $\pm q$ that are widely ...
- 1
3
votes
1
answer
236
views
Wilson Loops for Lattice Gauge Theory on $\subset\mathbb{Z}^2$ over the gauge group $\mathbb{Z}/n\mathbb{Z}\subset \mathbb{C}$
Is the potential complex valued?
I've simulated lattice gauge theory for a rectangular (finite) subset of $\mathbb{Z}^2$ over the gauge groups $\mathbb{Z}/n\mathbb{Z}$ (a.k.a. $\mathbb{Z}_n$) and $U(1)...
2
votes
2
answers
256
views
Covariant derivative of a Wilson line
Does the covariant derivative of a Wilson line given by $$W[A; z_0, z] = {\cal P}e^{-i\int^z_{z_0} dz ~A^af_{abc}}$$
vanish, i.e. $$D_zW[A; z_0, z] = 0~?$$
- 1,726
0
votes
0
answers
149
views
Exactly what value does the Wilson line take?
Let $G$ be the Lie group of a given theory with the Lie algebra $\mathfrak{g}$.
According to the Wikipedia article, a Wilson line is of the form
\begin{equation}
W[x_i,x_f]= P e^{i \int_{x_i}^{x_f} A}
...
- 1,741
2
votes
0
answers
119
views
Extracting a gauge-invariant variable from a given Wilson line? (NOT Wilson loop)
Let $W[x_i,x_f]$ be the Wilson line as defined here.
Under a local gauge transform $g(x)$, it transforms as
\begin{equation}
W[x_i,x_f] \to g(x_f)W[x_i,x_f] g^{-1}(x_i)
\end{equation}
which is shown ...
- 1,741
3
votes
0
answers
143
views
Wilson lines with Chan-Paton factors in string theory
In the context of compactifying the open string with Chan-Paton factors, Polchinski (Volume I Section 8.6) considers a toy example with a point particle of charge $q$ which has the action
$$ S = \int ...
- 1,418
1
vote
0
answers
120
views
Are pseudo Riemannian manifolds with identical Wilson loops isometric?
It is well established that in gauge theory, the Wilson loops of the theory determine the gauge potential up a gauge transformation. That is, two gauge potentials $A_\mu$ and $B_\mu $ produce the same ...
- 11
1
vote
1
answer
121
views
What is a non-linear space of connections
In the book "Loops Knots Gauge Theory and Quantum Gravity" when trying to define a loop representation, one needs to integrate over the space of connections (modulo Gauge transformations). ...
- 601
1
vote
1
answer
160
views
How does Witten's path integral know about changing crossings?
At a crossing of a knot, if I change the crossing by swapping the two lines, the knot is changed, along with its Jones Polynomial. Witten's path integral
$$
\int {D \mathcal{A}\ e^{i\mathcal{L}}\ W_R(...
- 143
0
votes
1
answer
171
views
Problems about "boundary conditions and topology"
In the book Field Theories of Condensed Matter Physics by Fradkin
In Page 311, when discussing the effects of boundary conditions on $Z_2$ lattice gauge theory, in the weak coupling phase, Fradkin ...
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