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.
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
\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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ02000009}
Linking options:
https://www.mathnet.ru/eng/tmf1277
https://www.mathnet.ru/eng/tmf/v102/i3/p420
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I. L. Buchbinder, A. P. Isaev, M. A. Podoynitsyin, S. A. Fedoruk, “Generalization of the Bargmann–Wigner construction for infinite-spin fields”, Theoret. and Math. Phys., 216:1 (2023), 973–999
I. L. Buchbinder, A. P. Isaev, M. A. Podoinitsyn, S. A. Fedoruk, “Generalized Wigner Operators and Relativistic Gauge Fields”, Phys. Part. Nuclei Lett., 20:4 (2023), 605
Ponomarev D., “3D Conformal Fields With Manifest Sl(2, C)”, J. High Energy Phys., 2021, no. 6, 055
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
Igor Bandos, M. Sabido, “Hamiltonian approach and quantization of D = 3,N=1 supersymmetric non-Abelian multiwave system”, J. High Energ. Phys., 2018:9 (2018)
J. A. de Azcárraga, S. Fedoruk, J. M. Izquierdo, J. Lukierski, “Two-twistor particle models and free massive higher spin fields”, J. High Energ. Phys., 2015:4 (2015)
Igor A. Bandos, “D=11massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries”, Nuclear Physics B, 796:1-2 (2008), 360
Igor A. Bandos, “Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach”, Physics Letters B, 659:1-2 (2008), 388
Mikhail Plyushchay, Dmitri Sorokin, Mirian Tsulaia, “Higher spins from tensorial charges and OSp(N|2n) symmetry”, J. High Energy Phys., 2003:04 (2003), 013
S Fedoruk, V.G Zima, “Uniform twistor-like formulation of massive and massless superparticles with tensorial central charges”, Nuclear Physics B - Proceedings Supplements, 102-103 (2001), 233
Igor Bandos, Jerzy Lukierski, Dmitri Sorokin, “Superparticle models with tensorial central charges”, Phys. Rev. D, 61:4 (2000)
V G Zima, S O Fedoruk, “Weinberg propagator of a free massive particle with an arbitrary spin from the BFV-BRST path integral”, Class. Quantum Grav., 16:11 (1999), 3653
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