described by UIRs of the so(1,4) algebra can be only fermions; 3) as a consequence of the AB symmetry, the vacuum condition can be consistent only for particles with the half-integer spin (in conventional units) and therefore only such particles can be elementary. In our approach the well known fact

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We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the non-relativistic domain (in fact for any symmetry group

to Pauli’s original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch-Gordan coefficients and the experimental evidence respectively, is presented. KEY WORDS: rotational invariance, bosons, fermions, spin-statistics. 1

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass spectrum of the corresponding charged sector, and a

We examine historic formulations of the spin-statistics theorem (and previous attempts at simple geometrical proofs) from a point of view that involves no quantum field theory. In particular, we make a critical analysis of concepts of particle identity, state distinguishability and permutation

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to “anomalous ” spin-statistics pairings for geons. However, in a sum

In this article, we begin with a review of Pauli’s version of the spinstatistics theorem and then show, by re-defining the parameter associated with the Lie-Algebra structure of angular momentum, that another interpretation of the theorem may be given. It will be found that the vanishing commutator

In this article, we begin with a review of Pauli’s version of the spinstatistics theorem and then show, by re-defining the parameter associated with the Lie-Algebra structure of angular momentum, that another interpretation of the theorem may be given. It will be found that the vanishing commutator

the distinguishing features are reversed. There is a fundamental spatial asymmetry between the relative orientations of any two vectors in a common frame of reference that persists even in the limit that the vectors coincide. For a pair of particles this asymmetry between their spin quantization frames renders them