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Elements of Phase Transitions and Critical Phenomena

Hidetoshi Nishimori and Gerardo Ortiz

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ... More


INITIAL DATA

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Only six out of ten Einstein field equations contain time derivatives and therefore represent the true evolution equations of the spacetime geometry. The remaining four equations are constraints that ... More


Harmonic Morphisms Between Riemannian Manifolds

Paul Baird and John C. Wood

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.001.0001
Subject:
Mathematics, Pure Mathematics

Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic ... More


Reduction techniques

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0013
Subject:
Mathematics, Pure Mathematics

When a map has a certain symmetry, the equations for a harmonic morphism reduce to equations in a smaller number of variables. Here, the appropriate symmetry is equivariant with respect to ... More


Harmonic morphisms defined by polynomials

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0005
Subject:
Mathematics, Pure Mathematics

This chapter establishes the Liouville-type theorem which asserts that any entire (i.e., globally defined) harmonic morphism from a Euclidean space of arbitrary dimension to a Euclidean space of ... More


The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More


Global Existence Theorems: Asymptotically Euclidean Data

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0015
Subject:
Mathematics, Applied Mathematics

This chapter shows how the Penrose transform can be used to prove global existence of solutions of various semilinear field equations. It outlines the foundation points of Friedrich's conformal ... More


Modern Supersymmetry: Dynamics and Duality

John Terning

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567639
eISBN:
9780191718243
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567639.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The book begins with a brief review of supersymmetry, the construction of the minimal supersymmetric standard model, and approaches to supersymmetry breaking. General non-perturbative methods are ... More


LUTTINGER LIQUIDS

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The bosonization technique is useful for solving the interacting problem and for extracting a certain number of properties such as power law behavior of the correlation functions. However, this ... 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


Self-dual Poincaré Metrics

Charles Fefferman and C. Robin Graham

in The Ambient Metric (AM-178)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.003.0005
Subject:
Mathematics, Geometry / Topology

As an application of the formal theory for Poincaré metrics, this chapter presents a formal power series proof of a result of LeBrun [LeB] asserting the existence and uniqueness of a real-analytic ... 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


The Ambient Metric (AM-178)

Charles Fefferman and C. Robin Graham

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.001.0001
Subject:
Mathematics, Geometry / Topology

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ... More


Spaces With Non-Euclidean Topology

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0011
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter presents a brief review of the Casimir effect in spaces with nontrivial topology (both flat and curved). As an important application of the numerous results obtained in this field, the ... More


The Roots of Reference

Timothy McCarthy

in Radical Interpretation and Indeterminacy

Published in print:
2002
Published Online:
November 2003
ISBN:
9780195145069
eISBN:
9780199833436
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195145062.003.0003
Subject:
Philosophy, Philosophy of Language

Applies the ‘Conformal Framework’ developed in Ch. 2 to some problems of the classical theory of reference, namely, to the question of how the reference of expressions in specific problem categories, ... More


The Ground of Logic

Timothy McCarthy

in Radical Interpretation and Indeterminacy

Published in print:
2002
Published Online:
November 2003
ISBN:
9780195145069
eISBN:
9780199833436
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195145062.003.0004
Subject:
Philosophy, Philosophy of Language

Applies the Conformal Framework to the philosophy of logic, and, in particular, to what McCarthy calls the Interpretation Problem for Logic, i.e. the problem of characterizing the logical devices of ... More


Theory of Quantum Hall States

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/9780199227259.003.07
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. FQH states cannot be described by Landau symmetry ... More


Lattice gauge theory beyond the Standard Model

Thomas Appelquist and Ethan T. Neil

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/9780199691609.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter gives an overview of methods and recent studies in the application of lattice gauge theory to physics beyond the standard model. It focuses on theories in which electroweak symmetry is ... More


Shape Dynamics: Relativity and Relationalism

Flavio Mercati

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198789475
eISBN:
9780191831294
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198789475.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Shape Dynamics is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity. The most important feature of this theory is the replacement of ... More


Introduction

Charles Fefferman and C. Robin Graham

in The Ambient Metric (AM-178)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter begins with a brief definition of conformal geometry. Conformal geometry is the study of spaces in which one knows how to measure infinitesimal angles but not lengths. A ... More


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