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

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.

References in corpus (8)

• Group field theory with non-commutative metric variables
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• From noncommutative kappa-Minkowski to Minkowski space-time
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Scalar field theory in Snyder space-time: alternatives
• On the $\star$-product quantization and the Duflo map in three dimensions
• Chern-Simons theory, Stokes' Theorem, and the Duflo map
• Quantum Mechanics on SO(3) via Non-commutative Dual Variables

Cited by in corpus (2)

• Group field theory condensate cosmology: An appetizer
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model