All the matrix elements of covariant tensor currents of massless particles in the covariant formulation

Abstract: We present an efficient algorithm for constructing all the matrix elements of covariant tensor currents of massless particles of arbitrary spins in the covariant formulation. The construction of matrix elements can be taken simply by assembling the basic matrix elements which are derived from the basic three-point vertices. We obtain the selection rules for the decay of an off-shell massive particle into two identical massless particles which are the generalization of the Landau-Yang (LY) theorem. After showing how to identify fully the discontinuity between the matrix elements for the spacelike and lightlike momentum transfers, we derive all the matrix elements of conserved tensor currents of massless particles including high spins, from which the Weinberg and Witten (WW) theorem is automatically extracted with additional limits on the particles.