Noncommutative Fourier transform for the Lorentz group via the Duflo map

2018/12/20 by Daniele Oriti, Giacomo Rosati
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Cotangent bundle #Fourier transform #Fundamental representation #Geometry #Group (periodic table) #Group representation #Lie algebra #Lorentz group #Lorentz transformation #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Political science #Pure mathematics #Quantum mechanics #Representation theory of the Lorentz group #Trigonometric functions #Unitary state #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.99.106005

published as Phys. Rev. D 99, 106005 (2019)

arxiv created 2018/12/20 · openalex publication_date 2019/05/13 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We defined a noncommutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the noncommutative Fourier transform ensuring the unitary equivalence with the standard group representation. Our construction is from first principles in the sense that all structures are derived from the choice of quantization map for the classical system, the Duflo quantization map.

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