New pseudoclassical model for Weyl particles.

It is demonstrated that the recently proposed pseudoclassical model for Weyl particles [1] (D.M. Gitman, A.E. Gonçalves and I.V. Tyutin, Phys. Rev. D 50 (1994) 5439) is classically inconsistent. A possible way of removing the classical inconsistency of the model is proposed. PACS number(s): 11.10.Ef, 03.65.Pm e-mail: [email protected] On leave from the Institute for High Energy Physics, Protvino, Moscow Region, Russia; e-mail: [email protected] In a recent paper [1], Gitman, Gonçalves and Tyutin proposed a new pseudoclassical model to describe a Weyl particle. The purpose of the present comment is to demonstrate that classically the model [1] is inconsistent. Namely, it will be shown that the model contains a classical relation of the form 0 = 1 being a consequence of the Lagrangian constraint, or, equivalently, of the corresponding secondary Hamiltonian constraint. A possible way of removing the classical inconsistency of the model is proposed. Let us consider the following relation in a superspace with real odd (Grassmann) variables ψ = ψ, a = 1, 2, . . . , N ,