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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


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