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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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Instantons in the Global $O(2)$ Model (Compact scalar field) - Polyakov textbook

This question is related with Polyakov, "Gauge Fields and Strings" section 4.2 In section 4.2, partition function is \begin{equation} Z=\sum_{n_{x,\delta}}\int_{-\pi}^{\pi}\prod_x\frac{d\...
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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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Lattice $SU(2)$ Higgs model in unitary gauge

I'm currently reading the book Quantum Fields on a Lattice by I. Montvay and G.Münster, and in section 6.1 they describe lattice actions for various higgs models. And I got confused at the moment ...
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Why the spectrum of square lattice with $\Phi=m \Phi_0$ with $m\in\mathbb{Z}$ is the same as $\Phi=0$?

In solid-state physics, in the study of square lattice in a perpendicular homogenous magnetic field, I have seen that when the flux per cell is an integer multiple of the flux quantum, i.e. $\Phi=m \...
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What means charge-$N$ scalar field $\varphi$?

Let $G = \oplus_{i=1}^N (\mathbb{Z}/N_i)$ be an Abelian group, for sake of simplicity eg a cyclic group $\mathbb{Z}/N$ . We consider abstract $G$- gauge theories. What is in this context the precise ...
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Charged excitations and Vortices in abstract Abelian Lattice Gauge theory

I have a question about heuristical interpretation of certain used terminology in the setting of abstract Abelian gauge theories as used in this paper by Chenjie Wang, Michael Levin. On page 4, Part A ...
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How do I numerically compute the interquark potential from the correlation function of Polyakov Loops?

I know that the potential can be calculated in the following way: $$ aV(r) =-\ln(<\sum_{\textbf{x}} (P(\textbf{x}+R)P^{\dagger}(\textbf{x}))>)/N_T. $$ Now, suppone I have some procudure to ...
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What is the conserved flux corresponding to center symmetry?

I understand the one-form symmetry of $U(1)$ gauge theories as related to the conservation of magnetic and electric flux, given by integration of two-form electromagnetic field tensor and its dual, ...
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Equivalence between magnetically perturbed Toric Code and 2D Transverse Field Ising model and Dispersion of 1 Quasiparticle spectrum?

Recently I was thinking how small local perturbations keep the topological order invariant in some Lattice Gauge Theories, like for the simplest one - Toric Code mode, which is defined as $$H_{TC} = ...
prikarsartam's user avatar
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Existence of Schwinger Functions for QCD?

It seems to me the 'naive' approach to proving the existence of Yang-Mills in a rigorous context (via Osterwalder-Schrader $\to$ Wightman axioms), would be: Study gauge invariant lattice QCD ...
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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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Topological classification of (classical, Abelian) vortices on a lattice

Consider the XY model on the square lattice. A field configuration $\theta$ is specified by an element of the Abelian group $\mathbb{R}/2\pi \simeq U(1)$ at each vertex of the lattice. The gradient of ...
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Why doesn't Peierls substitution capture the Lorentz force?

It's well known that the classical Hamiltonian governing the dynamics of a charged particle in a static magnetic field is $$ S_{cl}[x,\dot{x}] = \int_0^t dt' \frac{1}{2}m\dot{\vec{x}}^2 + e\vec{A}(x)\...
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How to update $SU(2)$ Higgs fields with Heat Bath algorithm?

I'm trying to update the Higgs field coupled with a pure gauge $SU(2)$ theory through Heat Bath algorithm. Pure gauge and Higgs configurations should be updated separately. For the pure gauge part the ...
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How to couple the Higgs field with $SU(3)$ (and/or $SU(2)$) Yang-Mills theory in numerical simulations?

I'm trying to couple the Higgs field to numerical simulations of pure gauge theory with heatbath and overrelaxation update of link variables. I don't know how to insert the Higgs field into the ...
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Can I do anything instructive by simulating QED on a lattice?

For learning something about the degrees of freedom and underlying path integral math, is it possible to do some kind of scalar QED or normal QED simulation on a lattice in the same way Lattice QCD is ...
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Resource recommendation for Kogut-Susskind Hamiltonian formalism for lattice gauge theory

Recently, quantum simulations for quantum field theories have been a hot topic of research. In these calculations, the lattice calculations are done using the Hamiltonian formalism in contrast to the ...
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Gauge degrees of freedom in Schwinger model

Schwinger model is the (1+1)-D QED. The number of gauge degrees of freedom (DOF) after the gauge fixing of the Schwinger model depends on the boundary condition of the model. For example, one can ...
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Which configurations are important in lattice QCD?

The failure of perturbation theory in describing strongly-coupled QCD is because it can't account for field configurations that are 'large'. My questions is: from experience in lattice QCD, what kind ...
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Can anyone suggest me some papers to understand the mathematics behind the form factor

I am trying to study semileptonic decays of $B$ mesons and different models are also there but I am not understanding how specific form factors are assigned to specific mesons. For example, right now ...
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Status of Approach of constructing Hamiltonians from Transfer Matrix

I am studying this old paper from J.B.Kogut on lattice gauge theories and spin systems [Rev. Mod. Phys. 51, 659(1979)]. This paper discusses about the way of constructing a quantum Hamiltonian using ...
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Meaning of lattice gauge theories

I would like to ask about the physical interpretation of lattice gauge theories. Coming from a condensed matter background, I know only that lattice gauge theories are constructed by adding additional ...
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Understanding fermion doubling in lattice QFT

I'm studying Rothe's book on lattice gauge theory. For the case of a scalar field, we can use lattice discretization to find (using equations 3.18 and 3.19 on page 41) $$\langle 0|T\phi(x)\phi(y)|0\...
Simplyorange's user avatar
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Dynamic field without kinetic term

I am trying to read a paper (https://arxiv.org/abs/2206.07725) that models electric and magnetic charges on a lattice model. But I am new to lattice theories, so I might be misunderstanding a lot of ...
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The "overlap function" of a $Z_2$ gauge theory

Consider a $Z_2$ gauge theory on a square lattice (Ising spins on edges) with classical degrees of freedom, i.e. \begin{equation} E = -\sum_{\square} \sigma_i\sigma_j\sigma_k\sigma_l \end{equation} ...
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How well does Lattice QCD handle relativity?

In Lattice QCD space-time is approximated by a grid. To me this doesn't seem to handle relativity well. Due to (1) A Lorentz transformation of the grid will distort the hyper-cube volumes into ...
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Continuum limit of lattice field theory

Just a simple question for lattice QCD experts, is continuum limit of lattice field theory a relativistic quantum field theory? Because i heard that lattice QCD is done in imaginary time, producing a ...
Peter's user avatar
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Is this condition $ \Phi=2\pi \frac mn =B \ell^2 $ correct for the magnetic flux per plaquette in 2D square lattice?

We have a 2D square lattice with the lattice constant $\ell$, and put it in a homogeneous magnetic field $B$. We are looking for the magnetic unit cell. As we know we get a periodic unit cell only ...
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Square lattice in the magnetic field; can someone please explain hopping factor Hofstadter uses?

If we have a square lattice in a homogenous magnetic field $\vec{B}=(0,0,B)$ and we use the Landau gauge for the magnetic potential $\vec{A}=(0,Bx,0)$; then, I have two questions: QUESTION $1$. Is the ...
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A square lattice in a homogeneous magnetic field B: How would it be the direction of the magnetic potential $A$ in the given picture?

I have an infinite square lattice that is placed in a homogenous magnetic field $B$ with vector potential $A$. My Question Can someone please explain/illustrate how it would be the direction and ...
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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 gauge theory with $A_\mu$ instead of $E_\mu$ or $B_\mu$

In most formulations of the lattice gauge theory one uses the Hilbert space basis defined by the eigenstates of the electric or magnetic field. For example, in the "electric basis" on one ...
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Path integral in Lattice gauge theory with fixed gauge really the same as without fixing the gauge?

In 1 the question why in lattice gauge theories with gauge group $G$, there was no need for gauge fixing to obtain finite path integrals was answered. Thus observables could be calculated as \begin{...
2000mg Haigo 's user avatar
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1 answer
182 views

Non-perturbative approach to high-energy physics

I know that main numerical approach to modeling high-energy physics events are Monte-Carlo event generators. But they are using perturbative description of collision and decay processes of particles. ...
Peter's user avatar
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Wilson loops as representations of the Lorentz group

Wilson loops in lattice $4d$ Yang-Mills theory are used to build various glueball states of different spins when they are applied to the vacuum. The spin dependence of such states is related with the ...
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Continuum Limit of Lattice QCD

I was trying to verify that the continuum limit of lattice QCD is indeed, regular old QCD, but I ran into an issue where when I tried to take the limit $a \rightarrow 0$ ($a$ is the lattice spacing), ...
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