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Behrends–Fronsdal Spin Projection Operator in Space-Time with Arbitrary Dimension

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Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 (LT-XII/QTS-X 2017)

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Abstract

On the basis of the Wigner unitary representations of the covering group \(ISL(2,\mathbb {C})\) of the Poincar’e group we construct spin-tensor wave functions of free massive particles with arbitrary spin. These wave functions automatically satisfy the Dirac–Pauli–Fierz equations. Spin-tensors of polarizations and conditions that fix the corresponding relativistic spin projection operators (Behrends–Fronsdal projection operators which determine the numerators in the propagators of fields of relativistic particles) are obtained. With the help of these conditions we find the generalization for relativistic spin projection operators for particles of arbitrary spins and for arbitrary space-time dimensions \(D>2\).

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Acknowledgements

This work was supported by Russian Science Foundation, grant 14-11-00598.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia

    A. P. Isaev & M. A. Podoinitsyn

  2. State University of Dubna, University street, 19, Dubna, 141980, Russia

    A. P. Isaev & M. A. Podoinitsyn

Authors
  1. A. P. Isaev
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  2. M. A. Podoinitsyn
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Corresponding author

Correspondence to A. P. Isaev .

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Editors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Isaev, A.P., Podoinitsyn, M.A. (2018). Behrends–Fronsdal Spin Projection Operator in Space-Time with Arbitrary Dimension. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_7

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