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 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 | ||||||
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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 |
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| 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 |
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| Date: | October 2008 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/4228 |
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