Continuum limit of lattice dynamics
type: Item
instance of: scholarly article
title: Continuum limit of lattice dynamics
zbMATH Open document ID: 0594.58055
DOI: 10.1016/0034-4877(85)90036-9
published in: Reports on Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: The starting point for quantum theory of interacting fields is usually the ''free'' or ''Fock'' representation of the algebra of physical observables. Next, when the cut-off in nonlinear terms is removed, it appears necessary to pass to another representation of this algebra. Such a procedure is unsatisfactory in some respects. Logically, the choice of a particular ''initial'' representation is unjustified. We cannot be sure that it is ''a good starting point''. Modifications (normal ordering, etc.) needed in originally ill-defined expressions are not physically clear. The change of representation is the main source of divergencies in quantum field theory. Is it possible to construct the quantum dynamics directly for algebras of observables, without any particular representation ? In this paper the author presents a scheme of such construction, based on finite lattice approximation. Transition from one Cauchy hypersurface in space-time to another (the evolution) is defined by passing with a lattice to the continuum limit.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T25
zbMATH DE Number: 3956070
zbMATH Keywords: representation theory
zbMATH Keywords: time evolution
zbMATH Keywords: free or Fock representation
zbMATH Keywords: quantum theory
zbMATH Keywords: quantum dynamics
zbMATH Keywords: lattice approximation
author: S. Zakrzewski
MaRDI profile type: Publication
full work available at URL: 0034-4877(85)90036-9
OpenAlex ID: W2065450582
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description: scientific article; zbMATH DE number 3956070