Introduction to Lattice QCD

Rajan Gupta

Home/Archive/arXiv

arXiv · hep-lat/9807028

Introduction to Lattice QCD

Rajan Gupta

View original source ↗Read source document ↗Export metadata ↓

Abstract

These notes aim to provide a pedagogical introduction to Lattice QCD. The topics covered include the scope of LQCD calculations, lattice discretization of gauge and fermion (naive, Wilson, and staggered) actions, doubling problem, improved gauge and Dirac actions, confinement and strong coupling expansions, phase transitions in the lattice theory, lattice operators, a general discussion of statistical and systematic errors in simulations of LQCD, the analyses of the hadron spectrum, glueball masses, the strong coupling constant, and the quark masses.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Rajan Gupta. 1998-07-11. Introduction to Lattice QCD. https://arxiv.org/abs/hep-lat/9807028

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Strong-coupling expansions from field-space Fourier duality in scalar lattice field theory

Dualities between quantum field theories provide useful descriptions of otherwise inaccessible parameter regimes. We develop a strong-coupling expansion for a class of Euclidean scalar field theories on a lattice by applying a Fourier transform to the local interaction term. We focus on a self-interacting $ϕ^4$ theory on a (periodic) hypercubic lattice in arbitrary dimension and derive a dual representation in which the strong-coupling regime of the original model is described by weak interactions of a generally nonlocal dual field. Using standard diagrammatic techniques, we obtain partially resummed approximations for the free-energy density and the momentum-space two-point function, including dual interaction vertices through nominal order $g^{-{8}}$ and $g^{-{10}}$ correspondingly. For $d=2$ and $d=3$, the resulting expressions agree well with Hamiltonian Monte Carlo simulations over the parameter ranges studied and provide complementary approximations with an overlap in the weak-to-intermediate coupling region. We also discuss the assumptions and limitations of the construction and illustrate its application to the Ising model.

hep-lat↗

arXiv2026

Renormalized Polyakov loop in accelerated gluodynamics

In this paper we investigate accelerated gluodynamics for a broad intervals of temperature and acceleration. Our study is carried out within lattice simulation in the co-moving reference frame parameterized by the Rindler coordinates. We developed the renormalization prescription that allowed us to calculate renormalized Polyakov loop as a function of coordinate in the Rindler spacetime. Using the data for the renormalized local Polyakov loop, we calculated spatial dependence of the static quark free energy and effective mass of static quark. Besides the Rindler coordinates, it is believed that accelerated gluodynamics can be approximated utilizing non-accelerated gluodynamics with a properly adjusted temperature gradient in accordance with the Tolman-Ehrenfest law. We compared these approaches for the observables under study. It was found that they agree quite well close to the critical temperature and demonstrate disagreement at higher temperatures. We believe that this disagreement might be attributed to the Tolman-Ehrenfest law corrections which appear in the Rindler gluodynamics.

hep-lat↗

arXiv2026

Continuous Hasenbusch transport towards gauge diffusion with fermions

Incorporating dynamical fermions is a central challenge for diffusion samplers of lattice gauge theories. We propose an analytic pseudofermion sampler based on continuous Hasenbusch transport as a component for gauge diffusion. The construction uses shifted linear solves and a finite-path correction, requiring neither explicit fermion determinant evaluation nor a learned pseudofermion model. We demonstrate the coupling in the two-flavour Schwinger model without neural networks, obtaining corrected physical observables compatible with independent references. We also show why accurate covariance transport can leave large weight fluctuations, tracing them to the backward transition density. This analysis leads to a correction based on the Wilson operator trace that reduces log-weight variance without changing the generated fields or increasing the number of Dirac operator applications. The predicted improvement is verified on previously unused gauge backgrounds. These results provide an analytic option for incorporating fermions in gauge diffusion and a guide to controlling its correction weights.

hep-lat↗