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Journal of Mathematical Physics : Nine theorems on the unification of quantum mechanics and relativity

By A. Kryukov

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Book Id: WPLBN0002169538
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 16 October 2008

Title: Journal of Mathematical Physics : Nine theorems on the unification of quantum mechanics and relativity  
Author: A. Kryukov
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Journal of Mathematical Physics Collection
Historic
Publication Date:
2008
Publisher: American Institute of Physics

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Kryukov, A. (2008). Journal of Mathematical Physics : Nine theorems on the unification of quantum mechanics and relativity. Retrieved from http://netlibrary.net/


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Description: A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincaré transformations is introduced. For a class of functions in H that are well localized in the time variable, the usual formalism of nonrelativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes the usual Schrödinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be “isometrically and equivariantly embedded” into H. That is, classical space-time is isometrically embedded into H, Poincaré transformations have unique extensions to isomorphisms of H, and the embedding commutes with Poincaré transformations.

 

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