All Questions
Tagged with gauge-theory wilson-loop
58
questions
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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}
...
- 1,669
2
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58
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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 ...
- 1,669
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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 ...
- 1,378
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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 ...
1
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1
answer
46
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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). ...
- 368
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27
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Physical meaning of the Wilson Loops as spin impurities
This is in reference to the paper of David Tong here. In this paper in section 2, it says
In this first section, we explain how spin impurities, coupled to bulk gauge fields, can
be thought of as ...
- 1,200
7
votes
1
answer
277
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Gauge theories, boundaries and Wilson lines
My understanding of Wilson loops
Let's work with classical electromagnetism. The 4-potential $A_\mu$ determines the electric and magnetic fields, which are the physical entities responsible for the ...
- 4,827
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Relationship between holonomy and fundamental group
In my notes of topological QFT we demonstrated that the holonomy associated with a path in $\mathbb{R}^3$ is invariant under smooth deformation of the path if the connection is flat.
Then I wrote:
If ...
- 167
1
vote
1
answer
99
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De Rham current associated with knot in abelian CS theory on a generic manifold
I'm studying TQFT and I'm stucked on this part of the paper of my teacher:
My teacher didn't explain a lot about it and I've never followed an advanced course on differential geometry or algebraic ...
- 167
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46
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Holonomy expansion for path deformation
A path deformation by $\epsilon^{\mu}(s)$ induces a variation of the connection $A'(s)=A(s)+\Delta A(s)$. I'm trying to obtain the first-order expansion of the holonomy $H_{\gamma}(A)=Pe^{i\int_{\...
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Representation of nonabelian Wilson line in terms of fermionic fields
Context:
The coupling action of a particle of charge $q$ to a $U(1)$ gauge field is given by
\begin{equation}
S = q \int d \tau A_\mu \left( X \right) \frac{dX^\mu(\tau)}{d \tau} = -i \ln W_q,
\tag{...
- 897
3
votes
1
answer
126
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Dressing an operator by Wilson line in Quantum Electrodynamic
I am reading a paper arXiv:1507.07921 which introduce gravitational dressing. The paper compare it to dressing in QED.
Consider the scalar QED lagrangian
$$\mathcal{L}=-\frac{1}{4}(F^{\mu\nu})^2-|D_\...
- 133
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Can one build Wilson lines in general relativity?
This question has two parts:
Firstly, I am curious if one can build Wilson lines as a 'parallel transport operator' in general relativity in direct analogy with what is done in gauge theory. For a ...
- 1,117
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Calculating a rectangular Wilson loop for the free photon
I'm studying Creutz's Quarks, gluons and lattices, in chapter 6 on page 33, we have the following exercise
Calculate a rectangular Wilson loop for the field theory of free photons. Using any ...
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Berry phase and Wilson loop
According to the definition, the Wilson loop is
\begin{equation}
W[\mathcal{C}] =\operatorname{Tr}\left[\mathcal{P} \exp\left\{i\oint _{\mathcal{C}} A_{\mu } dx^{\mu }\right\}\right]
\end{equation}
...
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