"Principle of Indistinguishability" and equations of motion for particles with spin
Abstract
In this work we review the derivation of Dirac and Weinberg equations based on a ``principle of indistinguishability'' for the (j,0) and (0,j) irreducible representations (irreps) of the Homogeneous Lorentz Group (HLG). We generalize this principle and explore its consequences for other irreps containing spin >= 1. We rederive Ahluwalia-Kirchbach equation using this principle and conclude that it yields O(p2j) equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG for a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j=1/2, there exists no Dirac-like equation for the (j,0) (0,j) representation nor for the (1/2,1/2) representation. We rederive Kemmer-Duffin-Petieau (KDP) equation for the (1,0) (1/2,1/2)(0,1) representation by this method and show that the (1,1/2) (1/2,1) representation satisfies a Dirac-like equation which describes a multiplet of j=3/2 and j=1/2 with masses m and m/2 respectively.
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