Alternative linear structures associated with regular Lagrangians. Weyl quantization and the Von Neumann uniqueness theorem

Details Alternative linear structures associated with regular Lagrangians. Weyl quantization and the Von Neumann uniqueness theorem Alternative linear structures associated with regular Lagrangians. Weyl quantization and the Von Neumann uniqueness theorem

2006-02-03

arxiv.org/abs/math-ph/0602011v1

Physics

Mathematical Physics

24 pages, 2 eps figures, iop latex

Scientific paper

We discuss how the existence of a regular Lagrangian description on the tangent bundle $TQ$ of some configuration space $Q$ allows for the construction of a linear structure on $TQ$ that can be considered as "adapted" to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.

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