Abstract
In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in A(dS) spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.
Highlights
Elementary particles propagating on Minkowski spacetime were classified by Wigner using the unitary irreducible representations of the Poincaregroup ISOð3; 1Þ [1](see [2] for more details in any dimension)
For massless particles there are two different representations; the familiar massless particles which describe particles with a finite number of degrees of freedom determined by representations of the Euclidean group ED−2 1⁄4 ISOðD − 2Þ, and the less-familiar massless particle [continuous spin particle (CSP)] which describes a particle with an infinite number of physical degrees of freedom per spacetime point characterized by the representations of the short little group SOðD − 3Þ, the little group of ED−2 [3]
Applying (2.12) into (2.8), and referring to the Appendix C, we find that Eq (2.8) can be reduced to ð∂ω · ∂ωÞφ 1⁄4 0, which is a tracelessness condition for a redefined CSP field
Summary
Elementary particles propagating on Minkowski spacetime were classified by Wigner using the unitary irreducible representations of the Poincaregroup ISOð3; 1Þ [1]. It is interesting to examine the relationship between the modified CSP action [16,17] and the (Fang-) Fronsdal-like equation [5] using a field redefinition in D dimensions, as well as the connection between the constrained formalism of the Schuster-Toro action [8] and the Metsaev action [16] in flat spacetime.
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