A connection between spin and statistics based on Galilean invariant delta functions

作者：Kobayashi Masanori^*; de Montigny Marc; Khanna Faqir C

来源：Journal of Mathematical Physics, 2010, 51(8): 083522.

DOI：10.1063/1.3456059

We define Galilean invariant delta functions by using the Takahashi formulation, which describes particles with arbitrary spin. The direct calculation of the Galilean invariant delta functions in the (N + 1)-dimensional Galilean covariant extended manifolds reveals that, for N odd, there exists a surface on which these delta functions vanish. This feature corresponds to the spacelike separation in the relativistic quantum field theory, and it enables us to discuss a connection between spin and statistics in the Galilean covariant theories. These results show that a spin-statistics connection holds for even-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with odd N >= 5. Likewise, we observe that there is no such connection for odd-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with even N >= 4. Thus, our results support the claim that there is no connection between spin and statistics in the usual nonrelativistic theory, for which N=4.

• 出版日期2010-8