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Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance ComputingLecture Notes of the Les Houches Summer School: Volume 93, August 2009$
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Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo

Print publication date: 2011

Print ISBN-13: 9780199691609

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199691609.001.0001

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Lattice field theory fundamentals

Lattice field theory fundamentals

Chapter:
(p.1) 1 Lattice field theory fundamentals
Source:
Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing
Author(s):

M. Pilar HernÁndez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199691609.003.0001

This chapter reviews the basic building blocks of the regularization of Quantum Field Theories (QFT) on a space-time lattice. It assumes some familiarity with QFT in the continuum. In an introductory section, the path integral formulation is reviewed, focusing on important aspects such as the transfer matrix, the relation of correlation functions and physical observables, the perturbative expansion, and the key issue of renormalization and the Wilsonian renormalization group. It then considers in detail the lattice formulation of scalar, fermion and gauge field theories, paying careful attention to their physical interpretation, and the continuum limit. The difficulty of discretizing chiral fermions is discussed in detail, and various fermion discretizations are described. The strong coupling expansion is introduced in the context of lattice Yang-Mills theory and the criteria for confinement and for the presence of a mass gap are presented. It concludes with a description of Wilson's formulation of lattice QCD and a brief overview of its applications.

Keywords:   Quantum Field Theory, Renormalization, Lattice Field Theory, Correlation Functions, Transfer Matrix, Perturbation Theory, Chiral Fermions, Strong Coupling Expansion, Confinement, Triviality, Hadron Spectrum

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