Mass as a relativistic quantum observable

¹ Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité propre du Centre National de la Recherche Scientifique, associée à l'Ecole Normale Supérieure et à l'Université de Paris Sud.) 24 rue Lhomond, F-75231 Paris Cedex 05, France
² Laboratoire Kastler Brossel (Unité de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associée au Centre National de la Recherche Scientifique.) , Université Pierre et Marie Curie, case 74, 4 place Jussieu, F-75252 Paris Cedex 05, France

Received: 12 December 1996
Accepted: 20 February 1997

Abstract

A field state containing photons propagating in different directions has a non-vanishing mass which is a quantum observable. We interpret the shift of this mass under transformations to accelerated frames as defining space-time observables canonically conjugated to energy-momentum observables. Shifts of quantum observables differ from the predictions of classical relativity theory in the presence of a non-vanishing spin. In particular, quantum redshift of energy-momentum is affected by spin. Shifts of position and energy-momentum observables however obey simple universal rules derived from invariance of canonical commutators.