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arXiv:0805.2859

Constructive physics

Yuri Ozhigov

Published May 19, 2008• 8 citations
arXivHTMLPDF

Abstract

Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
DOI
10.48550/arxiv.0805.2859

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The present work deals with the idea of a multi-time wave function, i.e. a wave function with N space-time arguments for N particles. Firstly, a careful derivation of the necessity of multi-time wave functions in relativistic quantum mechanics is given and a general formalism is developed. Secondly, the physical meaning of multi-time wave functions is discussed in connection with realistic relativistic quantum theories, in particular the "Hypersurface Bohm-Dirac" model. Thirdly, a first interacting model for multi-time wave functions of two Dirac particles in 1+1 space-time dimensions is constructed. Interaction is achieved by means of boundary conditions on configuration space-time, a mechanism closely related to zero-range physics. This is remarkable, as a restrictive consistency condition rules out various types of interaction and consequently no rigorous interacting model was known before. Fourthly, the model is extended to more general types of interaction and to the N-particle case. Higher dimensions are also discussed. Finally, the "Two-Body Dirac equations" of constraint theory are placed within the context of the multi-time formalism. In particular, the question of probability conservation is critically discussed, leading to further implications both for fundamental and applied questions.
This essay begins with considerations of the relational structure of a set of variables taken to represent a conceptual universe. A plausible argument is used to establish the necessity for a statistical description of any nonstatic set of such variables. A particular statistical description is then constructed based on a partition of the set of variables into two statistically independent sets. This statistical description is then shown to yield equations formally equivalent to familiar equations of thermodynamics, quantum mechanics, and classical mechanics. This mathematical development is strongly suggestive of a unified way of looking at several divergent fields of physics.