Questions tagged [lattice-gauge-theory]
The study of (particle physics) gauge theories on a spacetime that has been discretized into a lattice.
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Proof of commutation relation for lattice QFT
How do you prove the following commutation relation for the lattice QFT
\begin{equation}
[\phi(X),\Pi(y)]=\text{i}a^{-d}\delta_{x,y}\mathbb{I}?
\end{equation}
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How fermion doublers cause practical issues?
These days I learn about the lattice gauge theory, and in particular learned when one naively discretizes the fermion action, doublers, superfluous poles for a propagator, emerge. I wonder what issue ...
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Is it possible to have a compact abelian $U(1)$ lattice gauge theory on a non-compact manifold?
We have a compact lattice gauge theory if we let $A_{i}(n)\in[-\pi,\pi]$, and if we identify $A_{i}(n)\sim A_{i}+2\pi$. A simple lattice gauge theory in 2+1D then has an action
$$S=\sum_{x}1-\cos(F_{\...
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Polyakov loops and Wilson loops as order parameters
At zero temperature, the confinement/deconfinement criterion is the area/length law of the following non-local parameter called the Wilson loop:
\begin{eqnarray}
W=\text{Tr}\exp\left(\oint_CA_idx^i\...
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How do we derive the Hamiltonian of the Wilson Loop Action?
I'm reading Fradkin and Susskind's 1978 paper "Order and disorder in gauge systems and magnets" to try and understand how they derive the Hamiltonian for the U(1) compact lattice gauge theory. The ...
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How to find propagator for domain wall fermions
I am working on domain wall fermions right now and I am trying to understand how Luescher finds the propagator for the domain wall fermions in this review https://arxiv.org/abs/hep-th/0102028 on pages ...
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Definition of four-potential in lattice gauge theory
In Wen's book 'Quantum Field Theory of Many Body Systems' at chapter 6.4, he defines scalar potential on lattice sites while vector potential at lattice links in two dimensional square lattice. What ...
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Singularity of free energy in $\mathbb{Z}_2$ lattice gauge theory
I'm currently reading Kardar's Statistical physics of Fields. In the book, the $\mathbb{Z}_2$ lattice gauge theory is constructed as the dual of the 3d Ising model.
(Note: the Hamiltonian is $H = \...
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$\mathbb Z_N$ (discrete) gauge theory
I am currently trying to go through some literature on symmetry protected topological phases and gauge theories defined on lattices. I am looking for a mathematically precise reference that discusses $...
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Relation between Poisson equation and the Wilson lattice-gauge theory link variables
I've recently started writing a library of numerical solvers for elliptic partial differential equations, with particular focus on the Poisson equation. If one considers typical Poisson equation in ...
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How to write a naive Dirac matrix for Lattice QCD?
I'm trying to write down the naive Dirac matrix (with fermion doubling) for a LQCD simulation with one quark, for now. I initialized the $SU(3)$ gauge field and the quark field. The quak field has 4 ...
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Hadrons as partons? e.g. hadron distribution function inside another hadron
Parton distribution functions (PDFs) are typically seen as describing the probability that a parton, e.g. a quark or gluon, can be found in a hadron with particular momentum fraction $x$. They can be ...
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Lattice QCD $SU(3)$ Pseudo Heat Bath Algorithm in Practice
I'm doing a Lattice QCD project and would like to use the pseudo heat bath algorithm for updating links. I've been following Gattringer and Lang's "Quantum Chromodynamics on the Lattice". ...
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The heat bath algorithm for $SU(3)$ lattice gauge field
I'm studying lattice gauge theory and succeeded in simulating $U(1)$, $SU(2)$ with a heat bath algorithm. However, I have difficulty in applying the algorithm to $SU(3)$. I refer to Gattringer and ...
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$\mathbb{Z}_2$ gauge theory and disorder
I am confused about basics of $\mathbb{Z}_2$ (and likely other) gauge theories and plain disorder. Let
$$H=H_F + h\,H_{EM}$$
$$H_F = -t\sum_l (c^\dagger_l \sigma^z_{l,l+1} c_{l+1} + h.c.)$$
be (the '...
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