Breakdown of Casimir Invariance in Curved Space-Time

TL;DR

This paper demonstrates that Casimir invariants, traditionally used in flat spacetime, fail to remain invariant in curved spacetime under non-inertial motion and external fields, affecting particles from spin-1/2 to spin-2.

Contribution

It reveals the breakdown of Casimir invariance in curved spacetime and provides explicit expressions for various spins, highlighting physical implications for particle propagation.

Findings

Casimir scalar invariance fails in non-inertial, curved spacetime.

External fields alter the invariance of spin Casimir scalars.

Non-inertial motion induces an effective mass for spin interactions.

Abstract

It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincare 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 co-ordinates 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 spin-3/2 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.