Job A. Nable | Searcharxiv

arXiv2019

Moyal Star-Product and Unitary Representations of the Euclidean Motion Group

In this paper, the Moyal star-product quantization is used to construct the unitary irreducible representations of the Euclidean motion group on 3-dimensions. These unitary representations will come from the representation of its Lie algebra whose operators are defined by the left Moyal star-product multiplication. In fact, these representations of the Lie algebra is the infinitisimal representation. Hence, the exponentiation of these operators gives rise to unitary operators that defines the desired unitary representations.

math-ph↗

arXiv2017

Deformation quantization in the teaching of Lie group representations

In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization method of classical mechanics and is an autonomous approach to quantum mechanics, arising from the Wigner quasiprobability distributions and Weyl correspondence. We advertise the utility and power of deformation theory in Lie group representations. In implementing this idea, many aspects of the method of orbits is also learned, thus further adding to the mathematical toolkit of the beginning graduate student of physics. Furthermore, the essential unity of many topics in mathematics and physics (such as Lie groups and Lie algebras, quantization, functional analysis and symplectic geometry) is witnessed, an aspect seldom encountered in textbooks, in an elementary way.

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