Relativistic schrödinger equation for a particle with arbitrary spin

N.J. Ionescu-Pallas

P. M. Mathews

It is shown that a recently derived relativistic Schr\"odinger equation for free particles of arbitrary spin can be consistently quantized in the case of half-integer spins (but not for integer spins) by invoking the microcausality condition and using the role of certain expectation values of the $c$-number theory as generators of transformations of the Poincar\'e group in the $q$-number theory. The correct type of statistics (Fermi-Dirac) for half-integer-spin particles is obtained as a consequence of the theory. The way to handle the integer-spin case is indicated, but details are left for future presentation.

Kwong-Chuen Tam

A quantum-mechanical wave equation for two particles of arbitrary spin is derived for any instantaneous interaction. The starting point is an integral equation which is a relativistic generalization of the SchrOdinger integral equation and is similar to the Bethe-Salpeter equation. The final two-particle wave equation contains the sum of the Hamiltonians of the two particles and has only one time variable. It reduces to the two-particle Schrodinger equation in the non-relativistic limit

H. A. Mourad, I.Sh. Vashakidze

Ralph F. Guertin. Physics Department

P. M. Mathews

In a recent paper a relativistically covariant Schr\"odinger 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 Poincar\'e 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.