Non-commutative Fourier transform for the Lorentz group via the Duflo map
High Energy Physics - Theory
2019-05-22 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1812.08616,
title = {Non-commutative Fourier transform for the Lorentz group via the Duflo map},
author = {Daniele Oriti and Giacomo Rosati},
journal= {arXiv preprint arXiv:1812.08616},
year = {2019}
}