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Quantization as analysis in partial differential varieties

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Czechoslovak Journal of Physics B Aims and scope

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.

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Authors and Affiliations

  1. Department of Mathematics, MIT, 02139, Cambridge, Ma, USA

    I. E. Segal

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  1. I. E. Segal
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Additional information

Invited talk at the International Symposium “Selected Topics in Quantum Field Theory and Mathematical Physics”, Bechyně, Czechoslovakia, June 14–21, 1981.

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Segal, I.E. Quantization as analysis in partial differential varieties. Czech J Phys 32, 549–555 (1982). https://doi.org/10.1007/BF01596845

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  • DOI: https://doi.org/10.1007/BF01596845

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