Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields

TL;DR

The paper develops an ordinary-derivative, gauge-invariant framework for conformal totally symmetric bosonic fields of arbitrary spin in even dimensions $d\ge4$, introducing Stueckelberg and auxiliary fields and novel gauges (modified de Donder and de Donder-Stueckelberg). It proves the classical equivalence of this framework with the traditional higher-derivative formulation, clarifies the on-shell degrees of freedom, and presents a light-cone Lagrangian. By explicitly constructing gauge transformations and the conformal boost realization, the work reveals deep structural parallels with the gauge-invariant description of massive fields via a unified oscillator-based formalism. The de Donder-Stueckelberg gauge frame emerges as a practical tool to map between ordinary- and higher-derivative pictures and to relate conformal-field dynamics to massive-field gauge theories, with broad implications for higher-spin conformal theories and potential dualities. Overall, the paper provides a comprehensive, implementable route to handle conformal higher-spin bosons in a second-order, gauge-friendly setting, paving the way for interactions and BRST/unconstrained extensions.

Abstract

Conformal totally symmetric arbitrary spin bosonic fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative (ordinary-derivative) formulation for such fields is developed. We obtain gauge invariant Lagrangian and the corresponding gauge transformations. Gauge symmetries are realized by involving the Stueckelberg and auxiliary fields. Realization of global conformal boost symmetries on conformal gauge fields is obtained. Modified de Donder gauge condition and de Donder-Stueckelberg gauge condition are introduced. Using the de Donder-Stueckelberg gauge frame, equivalence of the ordinary-derivative and higher-derivative approaches is demonstrated. On-shell degrees of freedom of the arbitrary spin conformal field are analyzed. Ordinary-derivative light-cone gauge Lagrangian of conformal fields is also presented. Interrelations between the ordinary-derivative gauge invariant formulation of conformal fields and the gauge invariant formulation of massive fields are discussed.