The :ϕ⁴₄: quantum field theory, II. Integrability of Wick kernels

1996/08/17 by Edward P. Osipov, Osipov, Edward P.
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #advanced mathematical theories #funct-an #hep-th #math.FA

paper · pdf · doi:10.48550/arxiv.hep-th/9608115

56 pages, LaTeX

arxiv created 1996/08/17 · openalex publication_date 1996/08/17 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We continue the construction of the :ϕ⁴₄: quantum field theory. In this paper we consider the Wick kernel of the interacting quantum field. Using the complex structure and the Fock-Bargmann-Berezin-Segal integral representation we prove that this kernel defines a unique operator--valued generalized function on the space \Sc^α(\R⁴) for any α<6/5, i.e. the constructed quantum field is the generalized operator-valued function of localizable Jaffe class. The same assertion is valid for the outgoing quantum field. These assertions about the quantum field allow to construct the Wightman functions, the matrix elements of the quantum scattering operator and to consider their properties (positivity, spectrality, Poincare invariance, locality, asymptotic completeness, and unitarity of the quantum scattering).

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