Nonstandard spin 2 field theory

TL;DR

This paper explores alternative consistent theories for spin-2 fields beyond General Relativity by imposing specific constraints, leading to a parameterized family of theories that break certain symmetries.

Contribution

It introduces a new class of spin-2 field theories constrained to eliminate non-physical degrees of freedom, extending the linear Fierz-Pauli framework with a parameterized nonlinear order.

Findings

A consistent spin-2 theory is achieved with a constraint eliminating undesired components.

The theory is characterized by a parameter epsilon measuring symmetry breaking.

General Relativity is recovered as a limit when epsilon approaches zero.

Abstract

It is usually accepted that General Relativity is the only consistent theory which can be obtained starting from the linear Fiertz-Pauli Lagrangian. It is the aim of the present paper to study whether, under certain requirements, a different and consistent theory can be found. These requirements will be the common ones encountered in flat field theory: removal of the non physical degrees of freedom and conservation of the energy momentum currents determined by Noether's Theorem. It will be shown that imposing certain constraint (related to the elimination of the undesired components of the reducible representation) on the field manifold, a consistent theory (at least to first order in nonlinearties) is achieved. The theory obtained proceeding this way is characterizd, to the lowest nonlinear order, by certain parameter epsilon. General Relativity's corresponding term is found to be a limit case when the parameter tends to zero. So, epsilon measures at this level the size of the breaking of the global symmetry appearing in General Relativity i.e. diff.invariance. It remains as open questions the matters of the theory's solvability to all orders and the appearence of it's quantized version.