Relativistic spin equation and its generalization

Abstract

A relativistic wave equation for any spin is formulated by building up the second Casimir operator,wμwμ, of the Poincare group in an irreducible representation of Open image in new window , where ℒ is the spin part of the homogeneous Lorentz group and Open image in new window the orbital Poincare group. The wave equation in momentum space has the form [Γ μν p μ p ν − (a +bp2 + +cp+ + ...)]ϱ(p) = 0 whereΓ μν are matrices of infinite or finite dimensions according as the irreducible representation of − is unitary or not. Depending upon the values of the constants,a, b, c, ..., the equation may require solutions with unique spin or with definite mass-spin constraint. Explicit representations ofΓ μν are evaluated, and solutions to some simple problems are given as illustrations.