Multiple classical limits in relativistic and nonrelativistic quantum mechanics

Details Multiple classical limits in relativistic and nonrelativistic quantum mechanics Multiple classical limits in relativistic and nonrelativistic quantum mechanics

2009-07-22

arxiv.org/abs/0907.3943v1

J.Math.Phys.50:123512,2009

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

10.1063/1.3263939

The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a classical field behavior, showing that the limit $\hbar \to 0$ of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.

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