Abstract
Linearized gravity is considered as an ordinary gauge field theory. This implies the need for gauge fixing in order to have well-defined propagators. Only after having achieved this, the most general mass term is added. The aim of this paper is to study of the degrees of freedom of the gauge fixed theory of linearized gravity with mass term. The main result is that, even outside the usual Fierz–Pauli constraint on the mass term, it is possible to choose a gauge fixing belonging to the Landau class, which leads to a massive theory of gravity with the five degrees of freedom of a spin-2 massive particle.
Highlights
In this paper we consider the theory of linearized gravity with mass term
The aim of this paper is to study of the degrees of freedom of the gauge fixed theory of linearized gravity with mass term
C (2017) 77:614 symmetry, with well-defined propagators by means of an invariant gauge fixing term; 2. adding a mass term, which breaks gauge invariance and which modifies the propagators, asking which are the constraints on the parameters in order that the massive, symmetry broken theory has well-defined propagators, namely without tachyonic unphysical poles induced by the mass term; 3. addressing, the question of the five dof, i.e. selecting amongst the solutions satisfying the previous requirements 1 and 2, those, if any, which display the correct number of dof, in the hope of going beyond FP theory, finding a model with a more general, less constrained mass term which displays five dof
Summary
In this paper we consider the theory of linearized gravity with mass term. In particular, we are concerned with the well-known problem of the counting of the degrees of freedom (dof). A different one is to add directly a mass term to an ill defined theory, where the propagators are not defined ab initio because of the presence of a gauge symmetry, and realizing that the resulting theory is affected by several problems. Adding a mass term, which breaks gauge invariance and which modifies the propagators, asking which are the constraints on the parameters in order that the massive, symmetry broken theory has well-defined propagators, namely without tachyonic unphysical poles induced by the mass term; 3. 3 we briefly summarize the results of our previous work [14], listing the (eight) possibilities for a theory of a massive symmetric rank-2 two tensor field with well-defined propagators, free of unphysical tachyonic poles.
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