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arXiv · 2510.05011

Lorentz covariant on-shell cubic vertices for continuous-spin fields and integer-spin fields

R. R. Metsaev
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Abstract

In the framework of Lorentz covariant on-shell approach, interacting continuous-spin fields and integer-spin fields in flat space are investigated. Continuous-spin fields are considered by using a Lorentz vector superspace formulation, while integer-spin fields are considered by using an oscillator formulation. All parity-even cubic vertices for self-interacting continuous-spin fields realized as functions on the Lorentz vector superspace are obtained. Cross-interactions of continuous-spin fields and integer-spin fields are also derived. Several representatives of cubic vertices realized as distributions are obtained. We show that manifestly Lorentz invariant formal cubic action involving at least one continuous-spin field turns out to be divergent. We find the modification of such action which maintains Lorentz invariance and leads to finite cubic action. One-to-one correspondence of Lorentz covariant cubic vertices and light-cone gauge cubic vertices is demonstrated explicitly.

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R. R. Metsaev. 2025-10-06. Lorentz covariant on-shell cubic vertices for continuous-spin fields and integer-spin fields. https://arxiv.org/abs/2510.05011

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