ar X iv : 0 90 2 . 06 29 v 2 [ he p - th ] 1 1 M ar 2 00 9 Breakdown of Casimir Invariance for Elementary Particles in Curved Space - Time

Abstract. It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincaré group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear coordinates are used to describe the momentum generators within a Fermi normal co-ordinate framework. Specific expressions of the Casimir scalar properties are presented for spin-1/2 to spin-2 particles inclusive. While the Casimir scalar for linear momentum remains a Lorentz invariant in the absence of external fields, this is no longer true for the spin Casimir scalar. Potential implications are considered for the propagation of photons, gravitons, and gravitinos as described by the spin3/2 Rarita-Schwinger vector-spinor field. In particular, it is shown that non-inertial motion introduces a frame-based effective mass to the spin interaction, with interesting physical consequences that are explored in detail.