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Journal Article

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

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Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1812.08616.pdf
(Preprint), 486KB

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Citation

Oriti, D., & Rosati, G. (submitted). Non-commutative Fourier transform for the Lorentz group via the Duflo map.


Cite as: https://hdl.handle.net/21.11116/0000-0002-DC61-9
Abstract
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.