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Nine theorems on the unification of quantum mechanics and relativity

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


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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 non-relativistic 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 space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time 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
Kryukov, Alexey
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

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