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TOPOLOGICAL SIGMA MODELS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

String theory can be regarded, at the algebraic level, as a two-dimensional conformal field theory coupled to two-dimensional gravity. When the conformal field theory is also a topological field ... More


Integrability in sigma-models

K. Zarembo

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/9780198828150.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The following topics are covered in this chapter: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and ... More


Integrability in 2D fields theory/sigma-models

Sergei L. Lukyanov and Alexander B. Zamolodchikov

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/9780198828150.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This is a two-part course about the integrability of two-dimensional non-linear sigma models (2D NLSM). In the first part general aspects of classical integrability are discussed, based on the O(3) ... More


Interacting boson systems

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.03
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive ... More


Dynamical Mean-field Theories of Correlation and Disorder

E. Miranda and V. Dobrosavljević

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first ... More


Quantum field theory: Asymptotic safety

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 15 examines the conditions under which it is possible to define renormalized quantum field theories (QFTs) consistent on all scales (a property not necessary for effective QFTs and not shared ... More


O(N) vector model in the ordered phase: Goldstone modes

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 10 examines the case of the spontaneous breaking of a continuous symmetry. When there is spontaneous symmetry breaking, the correlation length diverges at all temperatures in the ordered ... More


Quantum field theory: An effective theory

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 8 discusses effective field theory. This concept is inspired by the theory of critical phenomena in statistical physics and based on renormalization group ideas. The basic idea behind ... More


Statistical Mechanics and Quantum Field Theory

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/9780199678839.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The connection between statistical mechanics on the one side and quantum mechanics and quantum field theory on the other side is based on the analogy between thermal and quantum fluctuations. ... More


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