Relativistic spin-statistics connection and Kaluza-Klein space-time

Enrico Santamato, F. De Martini

J. Anandan

The non-relativistic formalism introduced by Berry and Robbins that naturally incorporates the spin-statistics connection is generalized relativistically. It is then extended to an arbitrary Kaluza-Klein space-time by using a generalization of the Schwinger treatment of angular momenta to the representations of an arbitrary Lie group. This leads, in this approach, to the inclusion of the `internal' quantum numbers in the spin-statistics connection on an equal footing with spin.

Aaron Bennett

Vu B Ho, Michael J Morgan

This paper analyses quantum mechanics in multiply-connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular momentum. In particular, quantum mechanics in compactified Kaluza - Klein spaces is examined. These compactified spaces give rise to an additional angular momentum which can adopt half-integer values and therefore, may be identified with the intrinsic spin of a quantum particle.

Yu. M. Shirokov

Géry de Saxcé

The aim of this paper is to revisit, in Souriau's book "Structure of Dynamical Systems", the chapter devoted to the geometric quantization where the justifications of important results and formulae are not given and are difficult to prove. After recalling the coadjoint orbit method and its application to the relativistic particle with spin, we state and prove two keystone theorems that allow to equip its prequantum manifold with the symplectic and contact structures. We apply them to the relativistic particle with spin 1/2, leading to the Dirac equation and the conservation of the probability current. We propose also an identity of conservation of the spin current and, invoking the Kaluza-Klein theory, a systematic construction of the symmetries of charge conjugation, parity transformation and time reversal which seems to us more convenient and readable than that of the classical presentations.