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Proceedings of the Samahang Pisika ng Pilipinas

Quantization of Poisson brackets of some polynomials using different ordering rules

Ramon Jose C. Bagunu, Eric A. Galapon

Published May 23, 2019• 0 citations
OpenAlex

Abstract

The Poisson bracket of some classical polynomials were quantized using different ordering rules. Obstructions to quantization were addressed by using the basis operators Tmn from Weyl ordering, Smn from the simplest symmetrization rule, and Bmn from Born-Jordan ordering. Different solutions were then obtained using the respective algebra of these operators.

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The Poisson bracket of some classical polynomials were quantized using different ordering rules. Obstructions to quantization were addressed by using the basis operators Tmn from Weyl ordering, Smn from the simplest symmetrization rule, and Bmn from Born-Jordan ordering. Different solutions were then obtained using the respective algebra of these operators.
Quantization under simplest symmetric ordering of classical monomials with negative integral exponents of momentum has been written in integral form. This integral representation not only proved useful in transforming Weyl quantization to symmetric ordering quantization, and vice versa. They also facilitate derivation of commutation relations among different operators involving inverse powers of momentum operator, relations which can be used in solving quantization problems for classical functions with singularity along the momentum axis.