# 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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### 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. ...
169 views

### 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 ...
1 vote
51 views

### 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), ...
47 views

### Lattice QCD Link Variables Meaning of $\mu$ and $\nu$

I'm currently coding a lattice QCD project and ran into an issue with my understanding. A link variable connecting two points could be in the $\mu$ or $\nu$ direction, for example, $U_\mu(x)$ goes ...
67 views

### Are the definitions of chirality in continuum QFT and the Nielsen-Ninomiya theorem equivalent?

I have seen two definitions of chirality in quantum field theory: According to the Wikipedia article, chirality is defined as whether a particle transforms under a left- or right-handed ...
61 views

### 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". ...
1 vote
42 views

### Gauss law with staggered fermions

I was wondering if someone could explain how to derive the discrete version of Gauss law in 1+1 QED using staggered Fermions. The result I am trying to reproduce is found in multiple references [see ...
1 vote
57 views

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### On-site symmetries can be gauged, but is a gaugeable symmetry necessarily on-site?

I've always liked lattice QFT because it's mathematically unambiguous and non-perturbative, but it does have two drawbacks: (1) the lattice is artificial, and (2) some features are messy. One of those ...
33 views

I am trying to understand the presence of complex hopping amplitudes in Hubbard-like lattice models. The hopping term features the so called "Peierls phase": $$- t\sum_{j=1}^L \left( c_{... 4 votes 0 answers 58 views ### What is the connection between vertex/spin models and gauge theory? In the usual formulation of lattice gauge theories, one considers gauge variables on the links of a lattice (often hypercubic) taking value in some representation of a gauge group, U_{ij} \in G. The ... 3 votes 1 answer 664 views ### Recommend books for learning lattice QCD I want to learn lattice QCD by myself, but I don't know how to start. Can you recommend some books for lattice QCD? 1 vote 0 answers 76 views ### Is it possible to have a compact abelian U(1) lattice gauge theory on a non-compact manifold? We have a compact lattice gauge theory if we let A_{i}(n)\in[-\pi,\pi], and if we identify A_{i}(n)\sim A_{i}+2\pi. A simple lattice gauge theory in 2+1D then has an action$$S=\sum_{x}1-\cos(F_{\...
Assume we define the locality of a theory in the following way: Assume we have a theory of real scalars, so this theory is non local if the action has terms like $$\int d^dx\,\phi(x)V(x-y)\phi(y).$$ ...