Exactly Solvable Quantum Mechanical Models with Infinite Renormalization of the Wave Function

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dc.creatorShvedov, O. Yu.
dc.date2000-09-05
dc.date.accessioned2026-07-07T10:53:26Z
dc.date.available2026-07-07T10:53:26Z
dc.descriptionThe main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate renormalization beyond perturbation theory. However, known models of constructive field theory do not contain such difficulties as infinite renormalization of the wave function. In this paper an exactly solvable quantum mechanical model with such a difficulty is constructed. This model is a simplified analog of the large-N approximation to the $Φϕ^aϕ^a$-model in 6-dimensional space-time. It is necessary to introduce an indefinite inner product to renormalize the theory. The mathematical results of the theory of Pontriagin spaces are essentially used. It is remarkable that not only the field but also the canonically conjugated momentum become well-defined operators after adding counterterms.
dc.description13 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/hep-th/0009036
dc.identifierhttp://arxiv.org/abs/hep-th/0009036
dc.identifierJ.Phys.A34:3483-3496,2001
dc.identifierdoi:10.1088/0305-4470/34/16/316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185484
dc.subjectHigh Energy Physics - Theory
dc.titleExactly Solvable Quantum Mechanical Models with Infinite Renormalization of the Wave Function
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