Theoretical and Mathematical Physics

, Volume 198, Issue 1, pp 89–99 | Cite as

Polarization Tensors for Massive Arbitrary-Spin Particles and the Behrends–Fronsdal Projection Operator

  • A. P. IsaevEmail author
  • M. A. PodoinitsynEmail author


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.


higher spin Wigner unitary representation Poincaré group Dirac–Pauli–Fierz equations Behrends–Fronsdal projection operator 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear PhysicsDubna, Moscow OblastRussia
  2. 2.Dubna State UniversityDubna, Moscow OblastRussia

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