EVENT DETAILS AND ABSTRACT

Title: The spin-statistics relation from nonrelativistic quantum mechanics
Speaker: Professor Jonathan Robbins
Speaker Info: U. Bristol and BRIMS, Hewlett-Packard Labs
Brief Description:
Special Note:
Abstract:

The spin-statistics relation states that the wavefunction of two identical particles in three dimensions is even (bosons) or odd (fermions) under particle exchange, according to whether the particle spin $S$ is integral or half-integral. Within quantum field theory, this connection between spin and statistics may be derived as a theorem. In nonrelativistic quantum mechanics, however, it is generally regarded as an independent postulate.

In the talk, a derivation of the spin-statistics relation is given within the framework of ordinary quantum mechanics. The derivation is based on an implementation of quantum kinematics in which exchanged configurations are regarded as identical (so that the configuration space is doubly connected), and spin is attached to space so as to incorporate identity and satisfy a geometric condition (parallel transport). The spin-statistics relation follows by requiring that wavefunctions be single-valued. The Pauli sign factor $(-1)^{2S}$ emerges as a geometric phase of topological origin.