Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories

TL;DR

This paper extends the mathematical framework of spin-projector operators to spin-3 fields, enabling the analysis of unitary, non-tachyonic particle propagation in Lorentz-invariant field theories with complex mixing.

Contribution

It provides a complete set of spin-projector operators for fields up to rank-3, facilitating the search for healthy, unitary theories with higher-spin fields.

Findings

Reanalysis of known theories using new projector operators

Identification of conditions for ghost and tachyon-free propagation

Framework for exploring new higher-spin field theories

Abstract

We complete the set of spin-projector operators for fields up to rank-3 by providing all operators connecting sectors with same spin and parity. In this way we can broaden the search for unitary and non-tachyonic particle propagation in quadratic lagrangian with inter-field mixing. We use the properties of projector algebra to reanalyze known theories and shed light towards new healthy ones. We do so with full control over the gauge constraints by working the form of the saturated propagator in an appropriate frame of reference.