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Three topics in renormalization and improvement

Anastassios Vladikas

in Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, August 2009

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199691609
eISBN:
9780191731792
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691609.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


THE JACOBIAN IN PATH INTEGRALS AND QUANTUM ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter gives a general path integral formulation of the quantum anomaly for chiral symmetry. The quantum anomaly is identified as the Jacobian arising from the symmetry transformation of path ... More


Symmetries And Renormalization

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with linear continuous symmetries corresponding to compact Lie groups because they imply interesting formal properties; consequences of discrete symmetries can also be studied but ... More


Conformal field theory

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The present chapter is an introductory account of the basic concepts and important consequences of conformal symmetry, i.e. the invariance under local scale transformations, in field theories ... More


Path integral and anomaly

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 4 presented a thorough investigation of the anomaly within perturbation theory. This chapter presents the nonperturbative view. Section 5.1 performs a chiral transformation of the path ... More


Renormalisation of Yang–Mills Theory and BRST Symmetry

Laurent Baulieu, John Iliopoulos, and Roland Sénéor

in From Classical to Quantum Fields

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198788393
eISBN:
9780191830310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788393.003.0018
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Detailed discussion of the renormalisation properties of gauge theories based on the BRST Ward identities. General discussion of possible anomalies. Gauge independence of observable quantities.


A rough guide to quantum electrodynamics

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0040
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Arguably the most important achievement of quantum field theory is quantum electrodynamics (QED), which describes the interaction between electrons and photons, and this theory is presented in ... More


Renormalisation II: Improving perturbation theory

Michael Kachelriess

in Quantum Fields: From the Hubble to the Planck Scale

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198802877
eISBN:
9780191841330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802877.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces the quantum action as the generating functional of 1PI Green functions. The Ward identities of QED are derived and the vacuum polarisation is calculated. The renormalisation ... More


Variational Techniques of Many-Body Theory

Klaus Morawetz

in Interacting Systems far from Equilibrium: Quantum Kinetic Theory

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198797241
eISBN:
9780191838743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797241.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

The variational technique for nonequilibrium Green’s functions is derived resulting in the Hedin equations. This allows exploring of the high-density limit of diagrammatic expansions. Nonequilibrium ... More


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