2017/09/27 by Alexander J. Balsomo, Balsomo, Alexander J., Job A. Nable +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1709.09394
openalex publication_date 2017/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.