Correspondence between the first- and second-quantized theories of paraparticles

Abstract

It is shown that the parabosons and parafermions of the second-quantized parafield theory are equivalent to the finite-order paraparticles of the first-quantized theory. We follow the prescription of Hartle and Taylor which eliminates the redundancy of the generalized ray from the first-quantized formalism. For each statistical type of particle this allows us to establish an isomorphism between the state spaces of the two theories, in such a way that all corresponding observables have identical matrix elements for all states. This means that any system of finite-order particles can equally well be described by either the first- or the second-quantized formalism, in the same sense as applies to ordinary bosons and fermions. We analyze the different conclusions reached by other authors and explain the reasons for our disagreement.