Quantization = Integration over Function Space

  • James Glimm
  • Arthur Jaffe


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
$$ \int {A\;d\phi = \sum\limits_{G = graph} {I\left( G \right)} } $$
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.




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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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