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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Restoring Poincaré symmetries in Hamiltonian lattice field theories
I can imagine how the continuum limit of a non-relativistic quantum field theory discretized on a spatial lattice restores the Galilean symmetries of the original theory. But how does this work for ...
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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 ...
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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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A free parameter when switching from $\phi$ to $a$
In the unnumbered equation above (8) the authors of https://arxiv.org/abs/2109.05547 introduce a free parameter $m_x$ (presumably of mass dimension), when switching from the real scalar field $\phi$ (...
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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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Parity of a 1d Ising model, and with higher order terms
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\...
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Euclidean LQCD not on a lattice?
How much the idea of calculating Euclidean path integrals in LQCD is fundamentally tied to using formulations based on the discretized spacetime lattice?
In computational approaches to quantum many-...
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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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Is there a Majorana representation for toric code
Kitaev's toric code is known to be the Z2 gauge field theory, which suggests that there might exists a Majorana representation for the toric code, e.g., Majorana + Z2 gauge field. Hence, I wonder if ...
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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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Numerical simulations of standard model
Is standard model simulation a current and possible branch of research, or is it just lattice QCD?
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Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry
I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry
\begin{equation}
\mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
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Particle number in lattice field theory
Is it even possible to calculate a particle number of some field in lattice field theory? After all, it's implemented in the formalism of imaginary time path integrals, here's no such concepts as ...
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What is the reverse operation of gauging a global symmetry?
As far as I understand, gauging a global symmetry means taking a model with a global symmetry and transforming it into a model such that the previous symmetry group is now the gauge symmetry of your ...
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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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