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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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