Projection operator approach to the quantization of higher spin fields

TL;DR

This paper introduces a projection operator method to systematically construct free quantum fields for particles of arbitrary spin within a canonical Hamiltonian framework, enabling calculation of their fundamental quantum properties.

Contribution

It presents a novel approach using auxiliary multicomponent Klein-Gordon fields and differential operators to derive higher spin quantum fields and their properties.

Findings

Method allows calculation of (anti)commutation relations and propagators for higher spin fields.

Framework extends to interacting theories with known interaction Hamiltonians.

Fields transform under specific Lorentz group representations.

Abstract

A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein-Gordon field that satisfies canonical (anti)commutation relations and serves as an auxiliary higher spin field is introduced, and the physical higher spin field is obtained by acting on the auxiliary field by a suitable differential operator. This allows the calculation of the (anti)commutation relations, the Green functions and the Feynman propagators of the higher spin fields. In addition, canonical equations of motions, which are expressed in terms of the auxiliary variables, can be obtained also in the presence of interactions, if the interaction Hamiltonian operator is known. The fields considered transform according to the (n/2,m/2) + (m/2,n/2) and (n/2,m/2) representations of the Lorentz group.