Unitarity of Singh-Hagen Model in D Dimensions

Elias L Mendonça,R Schimidt Bittencourt

doi:10.1155/2020/8425745

Elias L Mendonça, R Schimidt Bittencourt

Open Access

https://doi.org/10.1155/2020/8425745

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Abstract

The particle content of the Singh-Hagen model (SH) in D dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding source terms, we provide a unitarity analysis in D dimensions. In addition, we have also analyzed the positivity of the massless Hamiltonian.

Highlights

The suggestion of a free theory describing higher spin particles dates back to 1936 by Dirac [1] and 1939 by Fierz and Pauli (FP) [2]
By mean of these projectors, Barnes and Rivers [3] have introduced a complete set of spinprojection operators which allows us to determine the particle content of a given rank-two field theory
By setting D = 3 + 1, we can recover the results of [8], and in this sense, we have a generalization of those projectors

Summary

Introduction

The suggestion of a free theory describing higher spin particles dates back to 1936 by Dirac [1] and 1939 by Fierz and Pauli (FP) [2]. Speaking about bosonic examples, it is quite simple to obtain the propagator of a rank-one field theory with the help of the transverse θμν = ημν − ωμν and longitudinal ωμν = ∂μ∂ν/□ operators By mean of these projectors, Barnes and Rivers [3] have introduced a complete set of spinprojection operators which allows us to determine the particle content of a given rank-two field theory (a slightly different basis is used by [4]). Some extensions of this set of projectors are given at [5, 6] where a new class of projection operators for three-dimensional models is constructed. By using the constraints as strong equalities, we provide the reduced Hamiltonian in terms of spin-projection operators demonstrating that the model carries only spin-3 particles and that it is positive definite

Rank-3 Spin-Projection Operators

On the Coefficients of the Spin-3 Singh-Hagen Theory

Unitarity of the Spin-3 Singh-Hagen Model

Hamiltonian Positivity of the Massless Case

Conclusion