Quantization of time using symmetric and Born-Jordan orderings

Authors

  • Daisy Arnado Romeo ⋅ PH Department of Mathematics and Natural Sciences, Cebu Institute of Technology University
  • Job A. Nable ⋅ PH Department of Mathematics, Ateneo de Manila University

Abstract

Quantization of a classical function, specifically time of arrival functions, may have different representations by using different orderings. In this paper we will be using the two common orderings, namely, symmetric and Born-Jordan orderings for distributions on the phase space  ℝ × S¹. These orderings are characterized by a real-valued function K such that K(0)=1. The function K is an additional integral factor of the standard Weyl quantization. These integral factors nultiplied by the Fourier transform of Weyl ordering will give the Fourier transforms of symmetric and Born-Jordan, respectively. Via the Wigner function, the method points to the determination of quasiprobability distributions corresponding to different orderings. This places the quantization scheme adopted here squarely within phase space quantum mechanics.

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Article ID

SPP-2020-3F-03

Section

Theoretical and Mathematical Physics

Published

2020-10-19

How to Cite

[1]
DA Romeo and JA Nable, Quantization of time using symmetric and Born-Jordan orderings, Proceedings of the Samahang Pisika ng Pilipinas 38, SPP-2020-3F-03 (2020). URL: https://proceedings.spp-online.org/article/view/SPP-2020-3F-03.