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## Introduction

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

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

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198702498.003.0001
- Subject:
- Mathematics, Mathematical Physics, Numerical Analysis

The first part of the introduction provides a (short) historical overview of Feynman’s development of his operational calculus, i.e. the formation of functions of several not necessarily commuting ... More

##
Expanding the *S*-matrix: Feynman diagrams

*Tom Lancaster and Stephen J. Blundell*

### in Quantum Field Theory for the Gifted Amateur

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0020
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces Feynman diagrams, which provide a wonderful pictorial way of visualizing terms in the perturbation expansion. Rather than evaluating umpteen integrals the chapter is able to ... 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

## Covariant Approaches to Quantum Gravity

*Claus Kiefer*

### in Quantum Gravity

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199212521
- eISBN:
- 9780191707377
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199212521.003.02
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

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

## Scalar field with λϕ4 interaction

*Michael Kachelriess*

### in Quantum Fields: From the Hubble to the Planck Scale

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198802877
- eISBN:
- 9780191841330
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802877.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The generating functionals Z[J] and W[J] for the λϕ4 theory are evaluated perturbatively and expressed through Feynman diagrams. The resulting Feynman rules are derived and the three basic one-loop ... More

## Applications

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0013
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Physical applications. Introduction of the scattering amplitude and cross sections. The phase space integrals. Explicit calculations of QED processes in the tree approximation. Derivation of the ... More

## The Euclidean Functional Integrals

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The Wick rotation and the functional integral in Euclidean space. Some mathematical theorems. Perturbation theory and Feynman rules in Euclidean space.

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