Open Access
2018 Deformation Quantization in the Teaching of Lie Group Representations
Alexander J. Balsomo, Job A. Nable
J. Geom. Symmetry Phys. 48: 79-100 (2018). DOI: 10.7546/jgsp-48-2018-79-100


We present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group ${\rm M}(2)$ 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 are 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 theory, quantization, functional analysis and symplectic geometry) is witnessed, an aspect seldom encountered in textbooks, in an elementary way.


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Alexander J. Balsomo. Job A. Nable. "Deformation Quantization in the Teaching of Lie Group Representations." J. Geom. Symmetry Phys. 48 79 - 100, 2018.


Published: 2018
First available in Project Euclid: 24 May 2018

zbMATH: 06944473
MathSciNet: MR3822801
Digital Object Identifier: 10.7546/jgsp-48-2018-79-100

Rights: Copyright © 2018 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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