Czechoslovak Journal of Physics B

, Volume 32, Issue 5, pp 549–555 | Cite as

Quantization as analysis in partial differential varieties

  • I. E. Segal
Article
Received:

Abstract

Replacing positive-energy considerations by considerations of invariance under theS-operator, and applying Paneitz' extension of the stability theory of the school of M. G. Krein, a long-sought canonical positive symplectic complex structure in the stable phase space of infinite-dimensional classical field-theoretic systems can be mathematically determined. This almost-Kählerization of the phase space then yields a (positive-definite) infinite-dimensional Riemannian structure that serves to specify formally, and convergently in finite-mode approximation, the physical vacuum measure for functional integrals involved in the associated quantized field. The method applies to a general class of nonlinear wave equations including that of Yang-Mills.

Keywords

Phase Space Wave Equation General Class Stable Phase Nonlinear Wave 
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Copyright information

© Academia, Publishing House of the Czechoslovak Academy of Sciences 1982

Authors and Affiliations

  • I. E. Segal
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

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