On the Hermitian projective line as a home for the geometry of Quantum Theory
| Autor: | Wolfgang Bertram, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov |
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| Přispěvatelé: | Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
pairs)
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences 01 natural sciences [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Quantum mechanics 0103 physical sciences 0101 mathematics Projective test Link (knot theory) Axiom Associative property Mathematical Physics Mathematics associative geometry 010308 nuclear & particles physics 010102 general mathematics Axiomatic system Lie group Mathematical Physics (math-ph) quantum theory generalized projective geometries Hermitian matrix Jordan algebras (-triple systems Projective line PACS 02.10.Hh 02.10.Ud 02.20.Bb 02.20.Tw 02.40.Dr 03.65.Ta |
| Popis: | In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum Theory. In the present note, we refine this proposition by discussing further structural features of Quantum Theory: the link with associative involutive algebras, and with Jordan-Lie and Lie-Jordan algebas. The associated geometries are (Hermitian) projective lines over an associative algebra; their axiomatic definition and theory will be given in subsequent work with M. Kinyon. submitted to Proceedings of XXVII Workshop on Geometrical Methods in Physics, Bialowieza 2008 |
| Databáze: | OpenAIRE |
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