## 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