Abstract
Action principles for the single and double valued continuous-spin representations of the Poincaré group have been recently proposed in a Segal-like formulation. We address three related issues: first, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.
Highlights
Wigner showed that the unitary irreducible representations (UIRs) of the Poincare group are determined by those of the corresponding little group [1]
We introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally
We investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit
Summary
Wigner showed that the unitary irreducible representations (UIRs) of the Poincare group are determined by those of the corresponding little group [1]. The first goal of this paper is to explain how to derive the actions of bosonic and fermionic CSP gauge fields proposed in [9, 13] directly from the Fronsdal-like and FangFronsdal-like equations [8] by solving the trace-like constraints in the auxiliary Fourier space.. The first goal of this paper is to explain how to derive the actions of bosonic and fermionic CSP gauge fields proposed in [9, 13] directly from the Fronsdal-like and FangFronsdal-like equations [8] by solving the trace-like constraints in the auxiliary Fourier space.5 This includes HSP results from CSP ones by taking the appropriate helicity limit. These two appendices make use of standard facts about special functions summarised in the appendix E
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