Abstract
Based on theWigner unitary representations for the covering Poincaré group ISL(2,ℂ), we construct spin–tensor wave functions of free massive arbitrary-spin particles satisfying the Dirac–Pauli–Fierz equations. We obtain polarization spin–tensors and indicate conditions that fix the density matrices (Behrends–Fronsdal projection operators), which determine the numerators in the propagators of the fields of such particles. Using such conditions extended to the multidimensional case, we construct a generalization of Behrends–Fronsdal projection operators (for any number D >2 of space–time dimensions) corresponding to a symmetric representation of the D-dimensional Poincaré group.
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References
A. P. Isaev and M. A. Podoinitsyn, “Two-spinor description of massive particles and relativistic spin projection operators,” Nucl. Phys. B, 929, 452–484 (2018); arXiv:1712.00833v2 [hep-th] (2017).
E. P. Wigner, “On unitary representations of the inhomogeneous Lorentz group,” Ann. Math., 40, 149–204 (1939)
V. Bargmann and E. P. Wigner, “Group theoretical discussion of relativistic wave equations,” Proc. Nat. Acad. Sci. USA, 34, 211–223 (1948).
Yu. V. Novozhilov, Introduction to Elementary Particle Theory [in Russian], Nauka, Moscow (1972); English transl. (Intl. Series Monogr. Nat. Philos., Vol. 78), Pergamon, Oxford (1975).
N. N. Bogolubov, A. A. Logunov, A. I. Oksak, and I. T. Todorov, General Principles of Quantum Field Theory [in Russian], Nauka, Moscow (1987); English transl. (Math. Phys. Appl. Math., Vol. 10), Kluwer Academic, Dordrecht (1990).
Ya. B. Rumer and A. I. Fet, Group Theory and Quantized Fields [in Russian], Nauka, Moscow (1977).
S. Weinberg, “Feynman rules for any spin,” Phys. Rev., 133, B1318–B1332 (1964); “Feynman rules for any spin: II. Massless particles,” Phys. Rev. B, 134, 882–896 (1964).
P. A. M. Dirac, “Relativistic wave equations,” Proc. Roy. Soc. London Ser. A, 155, 447–459 (1936).
M. Fierz, “Über den Drehimpuls von Teilichen mit Ruhemasse null und beliebigem Spin,” Helvetica Phys. Acta, 13, 45–60 (1940).
M. Fierz and W. Pauli, “On relativistic wave equations for particles of arbitrary spin in an electromagnetic field,” Proc. Roy. Soc. London Ser. A, 173, 211–232 (1939).
R. E. Behrends and C. Fronsdal, “Fermi decay for higher spin particles,” Phys. Rev., 106, 345–353 (1957).
D. Ponomarev and A. A. Tseytlin, “On quantum corrections in higher-spin theory in flat space,” JHEP, 1605, 184 (2016); arXiv:1603.06273v3 [hep-th] (2016).
D. Francia, J. Mourad, and A. Sagnotti, “Current exchanges and unconstrained higher spins,” Nucl. Phys. B, 773, 203–237 (2007); arXiv:hep-th/0701163v2 (2007).
C. Fronsdal, “On the theory of higher spin fields,” Nuovo Cimento, 9, 416–443 (1958).
E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun. Math. Phys., 252, 189–258 (2004); arXiv:hep-th/0312171v2 (2003).
H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge Univ. Press, Cambridge (2015).
E. Conde and A. Marzolla, “Lorentz constraints on massive three-point amplitudes,” JHEP, 1609 (2016); arXiv:1601.08113v4 [hep-th] (2016).
E. Conde, E. Joung, and K. Mkrtchyan, “Spinor-helicity three-point amplitudes from local cubic interactions,” JHEP, 1608, 040 (2016); arXiv:1605.07402v2 [hep-th] (2016).
A. Marzolla, “The 4D on-shell 3-point amplitude in spinor-helicity formalism and BCFW recursion relations,” PoS(Modave2016), 002 (2017); arXiv:1705.09678v1 [hep-th] (2017).
A.-H. Nima, T.-C. Huang, and Y.-T. Huang, “Scattering amplitudes for all masses and spins,” arXiv: 1709.04891v1 [hep-th] (2017).
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This research was supported by the Russian Foundation for Basic Research (Grant No. 16-01-00562).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 198, No. 1, pp. 101–112, January, 2019. Received January 29, 2018.
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Isaev, A.P., Podoinitsyn, M.A. Polarization Tensors for Massive Arbitrary-Spin Particles and the Behrends–Fronsdal Projection Operator. Theor Math Phys 198, 89–99 (2019). https://doi.org/10.1134/S0040577919010069
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DOI: https://doi.org/10.1134/S0040577919010069