# On Lorentz-invariant spin-2 theories

## TL;DR

This paper systematically constructs and classifies Lorentz-invariant spin-2 theories, including new variants of Fierz-Pauli, massless, and partially massless models, by analyzing their Hamiltonian structure and degrees of freedom.

## Contribution

It introduces a broader class of Lorentz-invariant spin-2 theories through Hamiltonian analysis, extending known models like Fierz-Pauli and exploring partially massless cases.

## Key findings

- Classified theories based on degrees of freedom and constraints
- Identified wider classes of Fierz-Pauli and massless theories
- Discussed relations to known spin-2 theories

## Abstract

We construct Lorentz-invariant massless/massive spin-2 theories in flat spacetime. Starting from the most generic action of a rank-2 symmetric tensor field whose Lagrangian contains up to quadratic in first derivatives of a field, we investigate the possibility of new theories by using the Hamiltonian analysis. By imposing the degeneracy of the kinetic matrix and the existence of subsequent constraints, we classify theories based on the number of degrees of freedom and constraint structures and obtain a wider class of Fierz-Pauli theory as well as massless and partially massless theories, whose scalar and/or vector degrees of freedom are absent. We also discuss the relation between our theories and known massless and massive spin-2 theories.