On euclidean systems of covariance for massless particles

Domenico P. L. Castrigiano

Giuseppe Nisticò, Luigi Accardi, Guillaume Adenier +5 more

The known methods, due for instance to G.W. Mackey and T.F. Jordan, which exploit the transformation properties with respect to the Euclidean and Galileian group to determine the formalism of the Quantum Theory of a localizable particle, fail in the case that the considered transformations are not symmetries of the physical system. In the present work we show that the formalism of standard Quantum Mechanics for a particle without spin can be completely recovered by exploiting the covariance properties with respect to the group of Euclidean transformations, without requiring that these transformations are symmetries of the physical system.

Riccardo Falcone, Simon Fuchs

We investigate whether relativistic massless classical particles may emerge as the classical limit of massless quanta. To address this question independently of any specific dynamics, environment, or pointer basis, we develop an axiomatic and purely kinematical framework for the coarse-graining approach. In this formulation, a candidate classical phase space is taken as the outcome space of a POVM subject only to minimal classicality and covariance under the relevant spacetime symmetry group. Applying this framework to the Poincaré group, we prove a no-go theorem for massless particles: the covariance requirement is incompatible with the operational conditions for classicality. The theorem leaves open field-like limits of massless quanta, for example the emergence of electromagnetic or gravitational fields, while ruling out classical massless particles, such as classical photons or gravitons.

Roman Gielerak, Lech Jakóbczyk, Robert Olkiewicz

Stanley Gudder

Müge Boz, Namik Kemal Pak

The second order contribution for the relativistic scattering of massless spin-\\frac{1}{2} particles from an infinitely long solenoid, in the context of covariant perturbation theory, is calculated and shown to vanish. Thus, Born approximation is consistent for this case as well.