Spin Statistics Connection and Commutation Relations

S. Kamefuchi, Yoshinori Takahashi

J M Harrison, Jonathan M. Robbins

Gerhart Lüders, Bruno Zumino

The proof of the connection between spin and statistics for interacting fields is divided into two parts: commutation relations involving components of a single field, and commutation relations between different fields. The first problem is treated in this paper: the connection between spin and statistics is shown to follow from a few simple postulates. The explicit discussion is limited to the cases of spin zero and of spin one-half.

Takafumi Kita

A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $π$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.

R. O'Raifeartaigh, Colm A. Ryan

The method of the complete set is used to study a generalized commutation relation. This commutation relation is of interest for two reasons. First, it is very similar to the commutation relations considered by various authors in connection with generalized statistics. Secondly, it allows us to investigate further a problem previously considered by Wigner, namely, Do the equations of motion determine the quantum mechanical commutation relations? '' (auth)

FRANCESCO IACHELLO