Invariant Scalar Product and Observables in a Relativistic Theory of Particles of Arbitrary Spin

Abstract

In a recent paper a relativistically covariant Schrödinger equation was derived for particles of arbitrary spin $s$, locally covariant wave functions without redundant components being used to describe states of a particle. Here we determine the invariant scalar product with respect to which the representation of Poincaré transformations on these wave functions is unitary. It is shown that the conventional position and spin operators, not being Hermitian with respect to this scalar product, cannot be observables. New operators which can represent these observables are constructed with the aid of a generalized Foldy-Wouthuysen transformation which is determined explicitly for arbitrary spin.