Alternative linear structures for classical and quantum systems

Details Alternative linear structures for classical and quantum systems Alternative linear structures for classical and quantum systems

2007-06-12

arxiv.org/abs/0706.1619v1

Int.J.Mod.Phys.A22:3039-3064,2007

Physics

Quantum Physics

32 pages, two figures, to be published in IJMPA

Scientific paper

10.1142/S0217751X07036890

The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact 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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