Quantization = Integration over Function Space

  • James Glimm
  • Arthur Jaffe

Abstract

The construction of P(φ)2 fields begins with this chapter; Chapters 11–12 conclude the construction. We develop efficient methods for computing and estimating integrals
$$ \int {A\;d\phi = \sum\limits_{G = graph} {I\left( G \right)} } $$
(8.1.1)
of polynomials A = A(φ) with respect to a Gaussian measure dφ. There are a variety of equivalent methods for computing Gaussian integrals of polynomials, such as integration by parts, expansion in Hermite polynomials, or the use of annihilation and creation (raising and lowering) operators.

Keywords

Covariance 

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • James Glimm
    • 1
  • Arthur Jaffe
    • 2
  1. 1.Courant Institute for Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Harvard UniversityCambridgeUSA

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