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A guide to two-dimensional conformal field theory

Jörg Teschner

in Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School: Volume 106, June 2016

Published in print:
2019
Published Online:
September 2019
ISBN:
9780198828150
eISBN:
9780191866937
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198828150.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This is a review of two-dimensional conformal field theory including the Virasoro algebra, the bootstrap, and some of the relations to integrable models. An effort is made to develop the basic ... 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


Conformal Symmetry in Statistical Mechanics

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The core of the exposition of the theory of conformal symmetry in statistical mechanics are the concepts of correlation functions of order parameter fields, whose behaviour under conformal ... More


TWO-DIMENSIONAL FIELD THEORY AND BOSONIZATION

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/9780198529132.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomalies in two-dimensional field theory. Two-dimensional field theory is important in connection with conformal field theory and its applications to string theory ... More


Conformal Field Theory

Giuseppe Mussardo

in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Published in print:
2020
Published Online:
May 2020
ISBN:
9780198788102
eISBN:
9780191830082
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788102.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 10 introduces the notion of conformal transformations and the important topic of the massless quantum field theories associated to the critical points of the statistical models. The chapter ... More


Hamiltonian Systems Based on a Lie Algebra

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0010
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

There is a remarkable analogy between Euler’s equations for a rigid body and his equations for an ideal fluid. The unifying idea is that of a Lie algebra with an inner product, which is not ... More


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