History-like Path of Identical Particle Systems in Topological SpaceM Akhmad Aminuddin Bama

Abstract

In this paper, a new concept has been introduced related to the construction of inequivalent quantizations for a system, which is called “history-like path” for particles. This is a collection of non-causal homotopical paths. Each homotopy class of paths will be labelled with a “word” constructed from the generators of fundamental group pi1(QN(Ei)) of a configuration space of the system in a space-like Ei which is a deformation retract of M_i region that is a sub-space-time of M in which there is no singular slice (a slice M_c in M that contains a singular point). The labels determine the generators and their relations in constructing the fundamental group pi1(QN) of the system.