Differential operators on infinite dimensional space and quantum field theory

2012/02/20 by A. V. Stoyanovsky, Stoyanovsky, A. V.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1203.1253

openalex publication_date 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We conjecture that the renormalized perturbative S-matrix of quantum field theory coincides with the evolution operator of the standard functional differential Schrodinger equation whose right hand side (quantum local Hamiltonian) is understood as an element of an appropriate quantization of the Poisson algebra of classical field theory Hamiltonians. We show how to construct a quantization of this algebra, close to the algebra of differential operators on infinite dimensional space, but seemingly not appropriate for quantum field theory.

Citations

• The Poisson algebra of classical Hamiltonians in field theory and the problem of its quantization
• No-Counterterm approach to quantum field theory

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