ALTERNATIVE LINEAR STRUCTURES FOR CLASSICAL AND QUANTUM SYSTEMS

Author:

ERCOLESSI E.1,IBORT A.2,MARMO G.3,MORANDI G.4

Affiliation:

1. Physics Department, University of Bologna, CNISM and INFN, Via Irnerio 46, I-40126, Bologna, Italy

2. Depto. de Matemáticas, Univ. Carlos III de Madrid, 28911 Leganés, Madrid, Spain

3. Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinzia, I-80126 Napoli, Italy

4. Physics Department, University of Bologna, CNISM and INFN, V.le B. Pichat 6/2, I-40127, Bologna, Italy

Abstract

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 nonequivalent ways, "evading," so to speak, the von Neumann uniqueness theorem.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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