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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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Three topics in renormalization and improvement

Three topics in renormalization and improvement

Chapter:
(p.161) 3 Three topics in renormalization and improvement
Source:
Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing
Author(s):

Anastassios Vladikas

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199691609.003.0003

This chapter is a detailed presentation of three specific topics: (1) The consequences of the loss of chiral symmetry in the Wilson lattice regularization of the fermionic action, and its recovery in the continuum limit. The treatment of these arguments involves lattice Ward identities, through which we establish the normalization properties of lattice partially conserved currents and the relation between renormalized composite fields, like the scalar and pseudoscalar densities, which belong to the same chiral multiplet. We also discuss the consequences of the loss of chiral symetry for the chiral condensate. (2) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. In particular we present in detail the RI/MOM scheme. (3) The modification of the Wilson fermion action, by the introduction of a chirally twisted mass term, known as twisted mass QCD (tmQCD), which results to improved (re)normalization and scaling properties for physical quantities of interest.

Keywords:   Wilson fermion action and Ward identities, vector and axial current normalization, renormalization of composite fields, non-perturbative renromalization and RI/MOM, twisted mass QCD

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