Quantization of time using symmetric and Born-Jordan orderings


  • 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


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.



Article ID



Theoretical and Mathematical Physics



How to Cite

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.