ua nt - p h / 03 11 07 8 v 3 1 9 D ec 2 00 4 Spin , statistics , and the spin - quantization frame

The spin-statistics connection is derived in a simple manner under the postulate that the original and the exchange state vectors are only superposed with the plus sign. The single-particle state vectors must however exhibit dependence on the angle χ of rotations in spin space about the spin-quantization axis. This means that not only a spin-quantization axis but a complete quantization frame must be specified. In order to get the spinor ambiguity under control the exchange of the angles χ must be done by way of rotations in spin space and by admitting only rotations in one sense. The exchange vector then acquires the spin factor (−1) 2s. This works in Galilean as well as in Lorentz-invariant quantum mechanics. Quantum field theory is not required. 1 Introduction The symmetrization postulate of standard quantum mechanics, I recall, postulates that any state vector or wave function of a system of identical particles must be either symmetric or antisymmetric, that is, multiplied by either +1 or −1 when the state variables referring to any two particles are interchanged. There are thus two classes of systems, with different types of statistical distribution of energy among the particles: systems of bosons and systems of fermions. These two classes are connected with the spins of the particles: all particles which are known to be bosons are found to have integral spin, in units of ¯ h, while all known fermions have half-integral (i.e., half-odd-integral) spin. Within nonrelativistic quantum mechanics the connection with spin could not be proved and had here to be taken as another postulate. The first proof was provided by Pauli [1], who founded it on relativistic quantum field theory. This also remained the framework of the papers which in subsequent years refined and generalized Pauli's proof [2,3]. In 1965, however, Feynman in his Lectures [4] objected: