Kryukov, Alexey (2008) Nine theorems on the unification of quantum mechanics and relativity. [Preprint]

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Abstract
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 Poincare 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 Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski spacetime is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical spacetime is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations.
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Item Type:  Preprint  

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Additional Information:  To appear in: Journal of Mathematical Physics, vol. 49 issue 10 (2008)  
Keywords:  unification, quantum mechanics, relativity  
Subjects:  Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Quantum Field Theory 

Depositing User:  Alexey Kryukov  
Date Deposited:  13 Oct 2008  
Last Modified:  07 Oct 2010 15:17  
Item ID:  4228  
Subjects:  Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Quantum Field Theory 

Date:  October 2008  
URI:  http://philsciarchive.pitt.edu/id/eprint/4228 
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