منابع مشابه
Nambu Quantum Mechanics: A Nonlinear Generalization of Geometric Quantum Mechanics
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter’s moduli parameters are set to zero, the usual geometric formulation o...
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Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra. pacs 03.65.Bz, 03.65.Ca,11.15.Kc, 02.30.+g 1 Quaternion Quantum Mechanics Quantum mechanics defined over general algebras have been conjectured since 1934 [1]. In 1936 Birkoff and von Neumann noted that the p...
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In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
متن کاملA geometric approach to the canonical reformulation of quantum mechanics
Abstract The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be derived from the invariance of this line element in the canonical formulation. The canonical formulation of quantum statistical mechanics is also discu...
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Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However efforts to extend a similar type of reasoning to other areas of physics, namely electrodynamics, quantum mechanics and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2001
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(00)00052-8