E. Floratos, et. al. - work on 'Finite quantum mechanics' I would like to inform you that together with some collaborators in Greece and abroad we ponder about the intrinsic beauty of Number Theory and its role in Quantum Mechanics, so we have worked the past ten years trying to find some deeper connection. We think at this moment that merging quantum mechanics with number theory produces a new type of quantum mechanics which seems to us more fundamental, indeed it is a type of chaotic quantum mechanics with stronger connection to classical mechanics. Although we have not finalized our ideas about how this is done in detail we want to proceed further with examples and studies in various physical system of widespread interest (quantum computers, quantum Hall systems, black holes, string theory etc.) where the role of quantum mechanics and number theory is important. Please find below the complete list of papers where I am coauthor in this subject. E.G. Floratos, "The Heisenberg-Weyl group on the ZnxZn discretized torus membrane", Phys. Lett. B 233 (1989) 39. G.G.Athanasiu and G.G.Floratos, "Coherent States in Finite Quantum Mechanics" Nucl. Physics B 245 (1994) 343. G.G.Athanasiu and E.G.Floratos, "The light cone SUq(2) algebra as dynamical symmetry of the Azbel-Hofstadter problem", Phys. Letters B 352 (1995) 105. G.G.Athanasiu, E.G.Floratos and S.Nicolis, "Holomorphic quantization on the torus and finite quantum mechanics", J. Phys. A 29 (1996) 6737. E.G. Floratos and G.K. Leontaris, "Uncertainty relation and non-dispersive states in finite quantum mechanics", Physics Lett. B 412 (1997) 35. E.G. Floratos and S. Nicolis, "An SU(2) analog of the Azbel-Hofstadter Hamiltonian", J. Phys A 31 (1998) 3961. D. Ellinas and E.G. Floratos, "Prime decomposition and entaglement measure of finite quantum systems", J. Phys A 32 (1999) L63. G.G.Athanasiu, E.G.Floratos and S.Nicolis, "Fast Quantum Maps", J. Phys. A 31 (1998) L655. The paper "Coherent states in Finite Quantum Mechanics" with coauthor G.Athanasiu, contains the introduction and the literature on the subject. Important papers are the ones by M. Berry and different papers, using p-adic numbers by Meurice, which are refered in the above paper. The subject is developing slowly and the relations with number theory are in the areas of representations of groups over finite fields and special functions (orthogonal polynomials, modular functions, etc.) connected with finite fields. Also relations with quantum groups for deformation parameters with values roots of unity are emerging as well as relations with noncommutative geometry (recent paper by Witten and Vafa). It is also a natural physical language frame for Quantum Computers. It is not yet an established field by its own but I believe that the point of view of Finite Quantum mechanics as a framework for Quantum Systems with finite dimensional Hilbert spaces will be recognized gradually by the various related activities. All the references I send you contain number theoretic results of course of physics interest. Sincerely yours, Emmanuel Floratos. archive      tutorial      mystery      new      search      home      contact