## Externalist Cases and Internalist Theory

*Joseph Mendola*

### in Anti-Externalism

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199534999
- eISBN:
- 9780191715969
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534999.003.0002
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology

The dominant roots of externalism are the Twin Earth and Elm-Beech cases of Hilary Putnam, the Arthritis case of Tyler Burge, and the Feynman-Gell-Mann, Gödel-Schmidt, and Aristotle cases of Saul ... More

## GENESIS OF QUANTUM ANOMALIES

*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/9780198529132.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the history of quantum anomalies. The original indication of the anomaly appeared immediately after the modern formulation of field theory, namely, renormalization theory. ... More

## THE FEYNMAN PATH INTEGRAL AND SCHWINGER'S ACTION PRINCIPLE

*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/9780198529132.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter provides a brief introduction to the basics of quantum field theory. The basic ideas of Feynman path integrals and Schwinger’s action principle, a knowledge of which is required to ... More

## REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

*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/9780198529132.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum ... More

## LATTICE DYNAMICS

*A.M. Stoneham*

### in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

- Published in print:
- 2001
- Published Online:
- September 2007
- ISBN:
- 9780198507802
- eISBN:
- 9780191709920
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507802.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter examines the key approximations in crystal lattice dynamics in a way that is particularly helpful for defect studies. It discusses the Born-Oppenheimer approximation, the adiabatic ... More

## Coherent Interactions of Fields and Atoms

*Stephen C. Rand*

### in Lectures on Light: Nonlinear and Quantum Optics using the Density Matrix

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199574872
- eISBN:
- 9780191722219
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199574872.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

Chapter 5 begins the systematic application of the density matrix to describe optical interactions. First, stationary two‐ and three‐level atoms interacting with a traveling wave are compared to show ... More

## Climbing the Mountain: The Scientific Biography of Julian Schwinger

*Jagdish Mehra and Kimball Milton*

- Published in print:
- 2003
- Published Online:
- February 2010
- ISBN:
- 9780198527459
- eISBN:
- 9780191709593
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527459.001.0001
- Subject:
- Physics, History of Physics

Julian Schwinger was one of the leading theoretical physicists of the 20th century. His contributions are as important, and as pervasive, as those of Richard Feynman, with whom he shared the 1965 ... More

## Exploiting the Variational Principle

*Mike Finnis*

### in Interatomic Forces in Condensed Matter

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198509776
- eISBN:
- 9780191709180
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509776.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter begins with a discussion of the ubiquitous theorem that underlies much of the theory of interatomic forces, namely the Hellmann–Feynman theorem, and its derivation from the variational ... More

## FUNCTIONAL INTEGRALS

*Robert M. Mazo*

### in Brownian Motion: Fluctuations, Dynamics, and Applications

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199556441
- eISBN:
- 9780191705625
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556441.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses a different kind of integral, functional integrals or Wiener integrals. The idea of an integral over a space of functions is introduced. The way to define such an integral ... More

## Open Quantum Electrodynamics

*Heinz-Peter Breuer and Francesco Petruccione*

### in The Theory of Open Quantum Systems

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199213900
- eISBN:
- 9780191706349
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213900.003.12
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the ... More

## Anomalies in QFT

*Reinhold A. Bertlmann*

### in Anomalies in Quantum Field Theory

- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507628
- eISBN:
- 9780191706400
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507628.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter investigates the anomaly within standard mathematical techniques. It works predominantly in perturbation theory, calculating Feynman diagrams. It shows in detail the occurrence of the ... More

## The diversions of a gentle genius

*JAGDISH MEHRA and KIMBALL A. MILTON*

### in Climbing the Mountain: The Scientific Biography of Julian Schwinger

- Published in print:
- 2003
- Published Online:
- February 2010
- ISBN:
- 9780198527459
- eISBN:
- 9780191709593
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527459.003.0016
- Subject:
- Physics, History of Physics

In November 1973 the UCLA Monthly, a periodical for faculty and students of the University of California at Los Angeles (UCLA), published an interview with Julian Schwinger. Since the interview ... More

## Perturbative renormalization group: Explicit calculations

*Jean Zinn-Justin*

### in Phase Transitions and Renormalization Group

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter uses the assumptions introduced in Chapter 9 to show that it is indeed possible to find a non-Gaussian fixed point in dimension d = 4 - e, both in models with reflection and rotation ... More

## Statistical field theory: Perturbative expansion

*Jean Zinn-Justin*

### in Phase Transitions and Renormalization Group

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the perturbative calculation of correlation or vertex functions expressed in terms of field (functional) integrals. The successive contributions to the perturbative expansion ... More

## Quantum electrodynamics and Julian Schwinger’s path to fame

*JAGDISH MEHRA and KIMBALL A. MILTON*

### in Climbing the Mountain: The Scientific Biography of Julian Schwinger

- Published in print:
- 2003
- Published Online:
- February 2010
- ISBN:
- 9780198527459
- eISBN:
- 9780191709593
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527459.003.0007
- Subject:
- Physics, History of Physics

In the beginning of June 1947, the Shelter Island Conference was held in New York to discuss the fundamental problems of quantum mechanics, of which J. Robert Oppenheimer was the acknowledged leader. ... More

## Schwinger, Tomonaga, Feynman, and Dyson: the triumph of renormalization

*JAGDISH MEHRA and KIMBALL A. MILTON*

### in Climbing the Mountain: The Scientific Biography of Julian Schwinger

- Published in print:
- 2003
- Published Online:
- February 2010
- ISBN:
- 9780198527459
- eISBN:
- 9780191709593
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527459.003.0008
- Subject:
- Physics, History of Physics

Barely six months after the Shelter Island Conference, which reawakened his interest in quantum electrodynamics (QED), and just three months after returning to Harvard University from his extended ... More

## “There sweep great general principles which all the laws seem to follow”

*Marc Lange*

### in Oxford Studies in Metaphysics volume 7

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199659081
- eISBN:
- 9780191745201
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199659081.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter argues that science recognizes an important distinction: between conservation laws as constraints on the fundamental forces there could be, on the one hand, and conservation laws as ... More

## Topological Methods for Description of Quantum Many-Body Systems

*Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs*

### in Quantum Hall systems: Braid groups, composite fermions and fractional charge

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528708
- eISBN:
- 9780191713477
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528708.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter presents a topological description of quantum many-body systems within the Feynman path integration formalism. Configuration spaces for the system of two particles on the one-dimensional ... More

## Covariant approaches to quantum gravity

*Claus Kiefer*

### in Quantum Gravity: Third Edition

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199585205
- eISBN:
- 9780191739378
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199585205.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the important concept of the graviton. It discusses at some length linearized quantum gravity and its implications. A central role is played by path-integral quantization from ... More

## Feynman's Operational Calculus and Beyond: Noncommutativity and Time-Ordering

*Gerald W Johnson, Michel L. Lapidus, and Lance Nielsen*

- Published in print:
- 2015
- Published Online:
- September 2015
- ISBN:
- 9780198702498
- eISBN:
- 9780191772160
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198702498.001.0001
- Subject:
- Mathematics, Mathematical Physics, Numerical Analysis

This book provides an abstract theory of Feynman’s operational calculus for functions of (typically) noncommuting operators. Although it is inspired by Feynman’s original heuristic suggestions and ... More