Geodesic
Generalization of the Bargmann–Wigner construction for infinite-spin fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 76-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We generalize the Wigner scheme for constructing the relativistic fields corresponding to irreducible representations of the four-dimensional Poincaré group with infinite spin. The fields are parameterized by a vector and an additional commuting vector or spinor variable. The equations of motion for infinite-spin fields are derived in both formulations under consideration.
Keywords: unitary representations, massless infinite spin particles, relativistic fields. 
@article{TMF_2023_216_1_a5,
     author = {I. L. Buchbinder and A. P. Isaev and M. A. Podoynitsyin and S. A. Fedoruk},
     title = {Generalization of {the~Bargmann{\textendash}Wigner} construction for infinite-spin fields},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {76--105},
     year = {2023},
     volume = {216},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a5/}
}
TY  - JOUR
AU  - I. L. Buchbinder
AU  - A. P. Isaev
AU  - M. A. Podoynitsyin
AU  - S. A. Fedoruk
TI  - Generalization of the Bargmann–Wigner construction for infinite-spin fields
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 76
EP  - 105
VL  - 216
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a5/
LA  - ru
ID  - TMF_2023_216_1_a5
ER  - 
%0 Journal Article
%A I. L. Buchbinder
%A A. P. Isaev
%A M. A. Podoynitsyin
%A S. A. Fedoruk
%T Generalization of the Bargmann–Wigner construction for infinite-spin fields
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 76-105
%V 216
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a5/
%G ru
%F TMF_2023_216_1_a5
I. L. Buchbinder; A. P. Isaev; M. A. Podoynitsyin; S. A. Fedoruk. Generalization of the Bargmann–Wigner construction for infinite-spin fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 76-105. http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a5/

[1] E. P. Wigner, “On unitary representations of the inhomogeneous Lorentz group”, Ann. Math., 40:1 (1939), 149–204 | DOI | MR

[2] E. P. Wigner, “Relativistische Wellengleichungen”, Z. Phys., 124 (1948), 665–684 | DOI | MR

[3] V. Bargmann, E. P. Wigner, “Group theoretical discussion of relativistic wave equations”, Proc. Nat. Acad. Sci. USA, 34:4 (1948), 211–223 | DOI | MR

[4] A. Barut, R. Ronchka, Teoriya predstavlenii grupp i ee prilozheniya, v. 2, Mir, M., 1980 | DOI | MR | Zbl

[5] Yu. Shvinger, Chastitsy, istochniki, polya, v. 1, Mir, M., 1976 | DOI

[6] L. P. S. Singh, C. R. Hagen, “Lagrangian formulation for arbitrary spin. I. The boson case”, Phys. Rev. D, 9:4 (1974), 898–909 | DOI

[7] L. P. S. Singh, C. R. Hagen, “Lagrangian formulation for arbitrary spin. II. The fermion case”, Phys. Rev. D, 9:4 (1974), 910–920 | DOI

[8] C. Fronsdal, “Massless fields with integer spin”, Phys. Rev. D, 18:10 (1978), 3624–3629 | DOI

[9] J. Fang, C. Fronsdal, “Massless fields with half-integral spin”, Phys. Rev. D, 18:10 (1978), 3630–3633 | DOI

[10] P. Uest, Vvedenie v supersimmetriyu i supergravitatsiyu, Mir, M., 1989 | MR | Zbl

[11] I. L. Buchbinder, S. M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Superspace, IOP Publ., Bristol, 1998 | MR

[12] P. Schuster, N. Toro, “On the theory of continuous-spin particles: wavefunctions and soft-factor scattering amplitudes”, JHEP, 09 (2013), 104, 34 pp., arXiv: 1302.1198 | MR

[13] P. Schuster, N. Toro, “On the theory of continuous-spin particles: helicity correspondence in radiation and forces”, JHEP, 09 (2013), 105, 39 pp., arXiv: 1302.1577 | MR

[14] X. Bekaert, E. D. Skvortsov, “Elementary particles with continuous spin”, Int. J. Mod. Phys. A, 32:23–24 (2017), 1730019, 31 pp., arXiv: 1708.01030 | DOI | Zbl

[15] X. Bekaert, J. Mourad, “The continuous spin limit of higher spin field equations”, JHEP, 01 (2006), 115, 20 pp., arXiv: hep-th/0509092 | DOI | MR

[16] X. Bekaert, J. Mourad, M. Najafizadeh, “Continuous-spin field propagator and interaction with matter”, JHEP, 11 (2017), 113, 32 pp., arXiv: 1710.05788 | DOI | MR

[17] M. Najafizadeh, “Modified Wigner equations and continuous spin gauge field”, Phys. Rev. D, 97:6 (2018), 065009, 19 pp., arXiv: 1708.00827 | DOI | MR

[18] M. V. Khabarov, Yu. M. Zinoviev, “Infinite (continuous) spin fields in the frame-like formalism”, Nucl. Phys. B, 928 (2018), 182–216, arXiv: 1711.08223 | DOI | MR

[19] K. B. Alkalaev, M. A. Grigoriev, “Continuous spin fields of mixed-symmetry type”, JHEP, 03 (2018), 030, 24 pp., arXiv: 1712.02317 | DOI | MR

[20] R. R. Metsaev, “BRST-BV approach to continuous-spin field”, Phys. Lett. B, 781 (2018), 568–573, arXiv: 1803.08421 | DOI

[21] I. L. Buchbinder, S. Fedoruk, A. P. Isaev, A. Rusnak, “Model of massless relativistic particle with continuous spin and its twistorial description”, JHEP, 07 (2018), 031, 20 pp., arXiv: 1805.09706 | DOI | MR

[22] I. L. Buchbinder, V. A. Krykhtin, H. Takata, “BRST approach to Lagrangian construction for bosonic continuous spin field”, Phys. Lett. B, 785 (2018), 315–319, arXiv: 1806.01640 | DOI

[23] I. L. Buchbinder, S. Fedoruk, A. P. Isaev, V. A. Krykhtin, “Towards Lagrangian construction for infinite half-integer spin field”, Nucl. Phys. B, 958 (2020), 115114, 22 pp., arXiv: 2005.07085 | DOI | MR

[24] K. Alkalaev, A. Chekmenev, M. Grigoriev, “Unified formulation for helicity and continuous spin fermionic fields”, JHEP, 11 (2018), 050, 25 pp., arXiv: 1808.09385 | DOI | MR

[25] R. R. Metsaev, “Cubic interaction vertices for massive/massless continuous-spin fields and arbitrary spin fields”, JHEP, 12 (2018), 055, 75 pp., arXiv: 1809.09075 | DOI | MR

[26] I. L. Buchbinder, S. Fedoruk, A. P. Isaev, “Twistorial and space-time descriptions of massless infinite spin (super)particles and fields”, Nucl. Phys. B, 945 (2019), 114660, 25 pp., arXiv: 1903.07947 | DOI | MR

[27] R. R. Metsaev, “Light-cone continuous-spin field in AdS space”, Phys. Lett. B, 793 (2019), 134–140, arXiv: 1903.10495 | DOI | MR

[28] I. L. Buchbinder, M. V. Khabarov, T. V. Snegirev, Yu. M. Zinoviev, “Lagrangian formulation for the infinite spin $N=1$ supermultiplets in $d=4$”, Nucl. Phys. B, 946 (2019), 114717, 12 pp., arXiv: 1904.05580 | DOI | MR

[29] M. Najafizadeh, “Supersymmetric continuous spin gauge theory”, JHEP, 03 (2020), 027, 35 pp., arXiv: 1912.12310 | DOI | MR

[30] M. Najafizadeh, “Off-shell supersymmetric continuous spin gauge theory”, JHEP, 02 (2022), 038, 31 pp., arXiv: 2112.10178 | DOI | MR

[31] I. L. Buchbinder, S. A. Fedoruk, A. P. Isaev, V. A. Krykhtin, “On the off-shell superfield Lagrangian formulation of 4D, $\mathscr{N}=1$ supersymmetric infinite spin theory”, Phys. Lett. B, 829 (2022), 137139, 8 pp., arXiv: 2203.12904 | DOI | MR

[32] I. L. Buchbinder, S. A. Fedoruk, A. P. Isaev, “Light-front description of infinite spin fields in six-dimensional Minkowski space”, Eur. Phys. J. C, 82 (2022), 733, 11 pp., arXiv: 2207.02640 | DOI

[33] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR | MR | Zbl

[34] D. P. Zhelobenko, A. I. Shtern, Predstavleniya grupp Li, Nauka, M., 1983 | MR | Zbl

[35] A. P. Isaev, V. A. Rubakov, Theory of Groups and Symmetries. Representations of Groups and Lie Algebras, Applications, World Sci., Singapore, 2020 | MR

[36] A. P. Isaev, M. A. Podoinitsyn, “Two-spinor description of massive particles and relativistic spin projection operators”, Nucl. Phys. B, 929 (2018), 452–484, arXiv: 1712.00833 | DOI | MR

[37] S. Weinberg, “Feynman rules for any spin”, Phys. Rev., 133:5B (1964), B1318–B1332 | DOI | MR

[38] S. Weinberg, “Feynman rules for any spin. II. Massless particles”, Phys. Rev., 134:4B (1964), B882–B896 | DOI | MR

[39] V. G. Zima, S. A. Fedoruk, “Kovariantnoe kvantovanie $d=4$ superchastitsy Brinka–\allowbreakShvartsa s ispolzovaniem lorentsevykh garmonik”, TMF, 102:3 (1995), 420–445 | DOI | MR | Zbl