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Inverse problems and theoretical imaging

A Relativistic Wigner Function Affiliated with the Weyl-Poincaré Group

J. Bertrand, P. Bertrand

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-3-642-97177-8_21

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The authors obtain the phase-space quantisation for relativistic spinning particles. The main tool is what they call a 'Stratonovich-Weyl quantiser' which relates functions on phase space to operators on a suitable Hilbert space, and has the essential properties of covariance (under a group representation) and traciality. Their phase spaces are coadjoint orbits of the restricted Poincare group; they compute and explicitly coordinatise the orbits corresponding to massive particles, with or without spin. Some orbits correspond to unitary irreducible representations of the Poincare group; they show that there is a unique Stratonovich-Weyl quantiser from each of these phase spaces to operators on the corresponding representation spaces, and compute it explicitly.