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.
Highlights
The search for a theoretically consistent Lorentzinvariant massive graviton has been a challenging issue since 1939, when Fierz and Pauli (FP) proposed a linear theory of massive spin-2 field [1]
In this Appendix, we show that there is ghost if a system has two or more d.o.f. in the scalar sector
First we focus on the first two cases
Summary
The search for a theoretically consistent Lorentzinvariant massive graviton has been a challenging issue since 1939, when Fierz and Pauli (FP) proposed a linear theory of massive spin-2 field [1]. NARUKO, KIMURA, and YAMAUCHI initial conditions to solve the resultant differential equations are consistent with the number of DOFs in ghost-free theories This fact opens up a new direction of study for searching for new theories of a massive graviton, and it is worth revisiting the pioneering attempt by Fierz and Pauli as a starting point of constructing a theoretically consistent massive gravity. To this end, in the present paper, we construct the most general quadratic theory of a massive spin-2 field and a massless spin-2 field with Lorentz invariance in flat spacetime, based on the Hamiltonian analysis. We will provide an overview of the Hamiltonian formalism in Fourier space
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