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 TMF, 1995, Volume 102, Number 3, Pages 420–445 (Mi tmf1277)

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

V. G. Zima, S. A. Fedoruk

Kharkiv State University

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1995, 102:3, 305–322

Bibliographic databases:

Citation: V. G. Zima, S. A. Fedoruk, “Covariant quantization of $d=4$ Brink–Schwarz superparticle with using of Lorentz harmonics”, TMF, 102:3 (1995), 420–445; Theoret. and Math. Phys., 102:3 (1995), 305–322

Citation in format AMSBIB
\Bibitem{ZimFed95} \by V.~G.~Zima, S.~A.~Fedoruk \paper Covariant quantization of $d=4$ Brink--Schwarz superparticle with using of Lorentz harmonics \jour TMF \yr 1995 \vol 102 \issue 3 \pages 420--445 \mathnet{http://mi.mathnet.ru/tmf1277} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1348852} \zmath{https://zbmath.org/?q=an:0852.53065} \transl \jour Theoret. and Math. Phys. \yr 1995 \vol 102 \issue 3 \pages 305--322 \crossref{https://doi.org/10.1007/BF01017881} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ02000009} 

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This publication is cited in the following articles:
1. Buchbinder I.L., Fedoruk S., Isaev A.P., Rusnak A., “Model of Massless Relativistic Particle With Continuous Spin and Its Twistorial Description”, J. High Energy Phys., 2018, no. 7, 031
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