Wavefunctions of identical particles

Publisher Website
Google Scholar
Abstract
We present a description of the quantum mechanical states of a system of n indistinguishable particles moving on a manifold M by C/S2‐ valued functions ψ′ defined on the configuration space Mn/Sn. These functions satisfy one of two homotopy conditions, which characterize the particles as bosons or fermions. Any closed curve of Mn/Sn which does not intersect the diagonals can be classified as even or odd according to whether its lifts to Mn have end points in Mn which are even or odd permutations of each other. For bosons, ψ′ must map any such closed curve which also avoids kerψ′ onto an even number of basic loops of (C−{0})/S2. For fermions, ψ′ must map such even loops of Mn/Sn onto an even number, and odd loops onto an odd number, of basic loops of (C−{0})/S2.

This publication has 2 references indexed in Scilit: