Covariant quantization of $d=4$ Brink--Schwarz superparticle with using of Lorentz harmonics

V. G. Zima ; S. A. Fedoruk

Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 420-445

Résumé

Covariant first and second quantizations of the free $d=4$ massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of masslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with the correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that the harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized.