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Quantum Mechanics in Non'Inertial Frames with a Multi'Temporal Quantization Scheme: I) Relativistic Particles | | David Alba
; Luca Lusanna
; | | Date: |
22 Feb 2005 | | Subject: | hep-th astro-ph gr-qc | | Affiliation: | Firenze University) and Luca Lusanna (INFN, Firenze | | Abstract: | We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme in which the particles are quantized, but not the gauge variables describing the non-inertial frames: {it they are considered as c-number generalized times}. We study the coupled Schroedinger-like equations produced by the first class constraints and we show that there is {it a physical scalar product independent both from time and generalized times and a unitary evolution}. Since a path in the space of the generalized times defines a non-rigid non-inertial frame, we can find the associated self-adjoint effective Hamiltonian $hat{H}_{ni}$ for the non-inertial evolution: it differs from the inertial energy operator for the presence of inertial potentials and turns out to be {it frame-dependent} like the energy density in general relativity. After a separation of the relativistic center of mass from the relative variables by means of a recently developed relativistic kinematics, inside $hat{H}_{ni}$ we can identify the self-adjoint relative energy operator (the invariant mass) ${hat{cal M}}$ corresponding to the inertial energy and producing the same levels for the spectra of atoms as in inertial frames. Instead the (in general time-dependent) effective Hamiltonian is responsible for the interferometric effects signalling the non-inertiality of the frame but is not interpretable as an energy like in the case of time-dependent c-number external electro-magnetic fields. | | Source: | arXiv, hep-th/0502194 | | Services: | Forum | Review | PDF | Favorites | |
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