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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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