Symplectic geometry on the Hilbert phase space and foundations of quantum mechanics
- International Center for Mathematical Modeling in Physics, Engineering and Cognitive science, MSI, Vaexjoe University, S-35195 (Sweden)
We show that in the opposition to a rather common opinion quantum mechanics is not complete. It is possible to introduce so called hidden variable -- in our model classical fields -- and combine the statistical predictions of quantum mechanics with deterministic dynamics of those hidden variables. Quantum mechanics can be considered as an approximative description of physical processes based on neglecting by quantities of the magnitude o({alpha}), where {alpha} is the dispersion of fluctuations of the Gaussian background field. In this paper we present the detailed presentation of theory of infinite-dimensional phase space and derive main equations of quantum mechanics (e.g., Schroedinger's equation, Heisenberg's equation and von Neumann equation) from the Hamilton equation on the infinite-dimensional symplectic space. We emphasize (to escape misunderstanding) that our paper is not about quantization of systems with infinite number of degrees of freedom, but about representation of quantum systems as classical systems with infinite number of degrees of freedom. We also investigate the purely mathematical problem of preserving of the dispersion of Gaussian fluctuations by Hamiltonian flows.
- OSTI ID:
- 20798656
- Journal Information:
- AIP Conference Proceedings, Vol. 834, Issue 1; Conference: 2. conference on mathematical modeling of wave phenomena, Vaxjo (Sweden), 14-19 Aug 2005; Other Information: DOI: 10.1063/1.2205816; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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