Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

TL;DR

This paper develops a non-relativistic multi-temporal quantization scheme for particles in non-inertial frames, ensuring unitary evolution and the identification of inertial bound states, extending previous rigid frame results.

Contribution

It introduces a novel multi-temporal quantization approach for non-inertial frames in non-relativistic quantum mechanics, incorporating gauge variables as classical parameters.

Findings

Unitary evolution in all times achieved.

Inertial bound states can be identified after center of mass separation.

Results recover previous rigid frame quantization cases.

Abstract

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases.