Search for generalized, quantizable dynamical models
type: Item
instance of: scholarly article
title: Search for generalized, quantizable dynamical models
zbMATH Open document ID: 0665.46061
DOI: 10.1016/0034-4877(88)90031-6
author: Jerzy Rayski
published in: Reports on Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: A precisation of the quantization procedure using a separable Hilbert space and coherent states (of minimal dispersion in phase space) liberates quantum formalism of the difficulties connected with an infinite volume and continuous spectra. A regularization with or without a final transition with subsidiary masses to infinity is investigated, and consequences of a possible breakdown of unitarity are discussed. Gauge theories, even supplemented only by a global supersymmetry, bring about a partial regularization, i.e. some compensations of infinities, so that the theory acquires a status of superrenormalizability. Some alternatives of strings and superstrings, based on the old ideas of Peierls and McManus or Yukawa (nonlocal and bilocal fields) are investigated after a generally covariant reformulation. The resulting quantum fields no longer satisfy field equations of traditional form but are describable by an operator of evolution in time with a generalized prescription of ordering in time, and are expressible in a new picture intermediate between the Schrödinger and the Interaction pictures.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 4088314
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: coherent states
zbMATH Keywords: minimal dispersion
zbMATH Keywords: phase space
zbMATH Keywords: Gauge theories
zbMATH Keywords: global supersymmetry
zbMATH Keywords: superrenormalizability
zbMATH Keywords: field equations
zbMATH Keywords: ordering in time
zbMATH Keywords: new picture intermediate between the Schrödinger and the Interaction pictures
MaRDI profile type: Publication
full work available at URL: 0034-4877(88)90031-6
OpenAlex ID: W2084604553
cites work: A Convergent Expression for the Magnetic Moment of the Neutron
cites work: On the Invariant Regularization in Relativistic Quantum Theory
cites work: Q5787868
cites work: Q5792451
cites work: On differential conservation laws in non-local field theories
cites work: A λ ϕ 4 Quantum Field Theory without
cites work: Q3228389
Recommended article: Quest for Universal Integrable Models
Recommended article: Dynamical analysis of evolution equations in generalized models
Recommended article: On the quantization of constrained generalized dynamics
Recommended article: A Generalized Theory of Dynamical Trajectories
Recommended article: Search for high dimensional integrable models
Recommended article: Q5442745
Recommended article: Exactly solvable models and dynamic quantum systems
Recommended article: Theory of search for exact differential equations of dynamic processes
Recommended article: Trying to Characterize Robust and Generic Dynamics
Recommended article: A search for general principles of nonequilibrium physics
description: scientific article; zbMATH DE number 4088314