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Non-commutative Fourier transform for the Lorentz group via the Duflo map

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arxiv 1812.08616 v1 pith:DGART5SW submitted 2018-12-20 hep-th gr-qcmath-phmath.MP

Daniele Oriti , Giacomo Rosati This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords groupnon-commutativeduflofourierlorentzquantizationrepresentationtransform
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We defined a non-commutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the non-commutative 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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  1. A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors

    gr-qc 2025-01 conditional novelty 6.0 of 10

    A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.

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