New arbitrary-spin wave equations for (j, 0) ⊕ (0, j) matter fields without kinematic acausality and constraints

Following Weinberg, we note that for arbitrary spin the covariant spinors and the field operators can be constructed directly from Lorentz covariance. The propagator may then be defined as the vacuum expectation value of the time-ordered product of the field operators. We produce a new arbitrary-spin wave equation by inverting this propagator. The equation so produced, even at the free-particle level, is nonlocal. Explicit results for j = 1 are given and we have checked the procedure for j = 3 2 and 2 The equation does not support kinematically anomalous solutions, as do Weinberg's equations. In addition, unlike Weinberg's equations for integral spins, it has the particle and antiparticle spinors as its solutions for both fermions and bosons. No constraint equations, as required in the Rarita-Schwinger/Bargmann-Wigner formalism, are needed.