## A Game-Theoretic Perspective on Coalition Formation

*Debraj Ray*

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199207954
- eISBN:
- 9780191709104
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207954.001.0001
- Subject:
- Economics and Finance, Financial Economics

The formation of coalitions to achieve both collaborative and competitive goals is a phenomenon we see all around us. The list of examples of this phenomenon is long and varied: production cartels, ... More

## Coalitions, Cooperation and Noncooperation

*Debraj Ray*

### in A Game-Theoretic Perspective on Coalition Formation

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199207954
- eISBN:
- 9780191709104
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207954.003.0003
- Subject:
- Economics and Finance, Financial Economics

This chapter describes in greater detail what the phrases ‘cooperation within coalitions’ and ‘non-cooperation across coalitions’ mean in this book. It develops the idea of coalitional equilibrium, ... More

## Relativistic gases

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0025
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter repeats the derivation of the partition function for a gas, and hence of the other thermodynamic properties that can be obtained from it, but this time includes relativistic effects. It ... More

## Statement B and the Yang-Baxter Equation

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

### in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0019
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The ... More

## The partition function

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0020
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the partition function, which encodes all the information concerning the states of a system and their thermal occupation. Topics discussed include writing down the partition ... More

## Advanced Statistical Mechanics

*Barry M McCoy*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ... More

## CHERN–SIMONS THEORY AND KNOT INVARIANTS

*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/9780198568490.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More

## The Ising model in two dimensions: summary of results

*Barry M. McCoy*

### in Advanced Statistical Mechanics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes the many results of the exactly solved Ising model in two dimensions at H = 0 including: the partition function, free energy, spontaneous magnetization, the Toeplitz ... More

## Statistical mechanics of an ideal gas

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0021
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The partition function is a sum over all the states of a system of the relevant Boltzmann factors. Constructing the partition function is the first step to deriving all the thermodynamic properties ... More

## FLOWS AND FERROMAGNETS

*Geoffrey Grimmett*

### in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.003.0008
- Subject:
- Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More

##
Crystals and *p*-adic Integration

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

### in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0020
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes the properties of Kashiwara's crystal and its role in unipotent p-adic integrations related to Whittaker functions. In many cases, integrations of representation theoretic ... More

## PATH INTEGRALS IN QUANTUM MECHANICS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs the path integral associated with the statistical operator e -βH in the case of Hamiltonians of the simple form p2/2m + V (q). The path ... More

## Bimolecular reactions, transition-state theory

*Niels E. Henriksen and Flemming Y. Hansen*

### in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199203864
- eISBN:
- 9780191708251
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199203864.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses an approximate approach — transition-state theory — to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode ... More

## Irreversible Agreements: Symmetric Games

*Debraj Ray*

### in A Game-Theoretic Perspective on Coalition Formation

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199207954
- eISBN:
- 9780191709104
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207954.003.0005
- Subject:
- Economics and Finance, Financial Economics

This chapter studies a special case of the framework introduced in Chapter 4, one that relies on ‘symmetry’. It focuses on symmetric partition functions: such functions have the property that the ... More

## CLASSICAL AND QUANTUM STATISTICAL PHYSICS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter provides a simple physical interpretation to the formal continuum limit that has led, from an integral over position variables corresponding to discrete times, to a path integral. It ... More

## PATH INTEGRALS AND HOLOMORPHIC FORMALISM

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces the holomorphic representation of quantum mechanics, because it allows a study of the properties of boson systems both from the point of view of evolution and of quantum ... More

## PARTITION FUNCTION AND SPECTRUM

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0003
- Subject:

A direct application of the calculation of the partition function is provided by determining the spectrum of a Hamiltonian (which is assumed to be discrete, for simplicity). In this chapter, only ... More

## PATH INTEGRALS: FERMIONS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0007
- Subject:

The methods that have been described in previous chapters can be used to study general quantum Bose systems. They are based in a direct way on the introduction of a generating function of symmetric ... More

## Density operators and Wigner functions

*Helmut Hofmann*

### in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0019
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter introduces density operators and matrices for many-body systems, and explains their reduction to one- and two-body densities. Starting from the Slater determinant, the latter are ... More

## The chemical potential

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0022
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter extends the results on partition functions to systems in which the number of particles can vary. This allows the definition of the chemical potential and introduces the grand partition ... More