Tachyons and Representations of

Abstract

Lacking in the mathematical physics literature is a detailed treatment of tachyonic representations of the Poincaré group along lines similar to that for its real mass, positive and negative energy representations. Such representations Wigner did not consider in any detail in his 1939 paper on the unitary representations of the inhomogeneous Lorentz group (Wigner, Ann Math 40:149–204, 1939), and Bargmann and Wigner in their paper on the group theoretical classification of relativistic wave equations did not consider them either because “they are …unlikely to have a simple physical interpretation” (Bargmann and Wigner, Proc Nat Acad Sci (USA) 34(5):211–223, 1948). We are making a detailed study of tachyonic representations of the Poincaré group in four space-time dimensions and we describe some of our results here. In particular, we relate tachyonic representations of the Poincaré group to representations of the anti-de Sitter group, in a way analogous to the way in which positive energy, real mass representations of the Poincaré group are related to unitary principal series representations of the de Sitter group via group contraction and deformation.