Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz-Pauli massive gravity). (English) Zbl 1354.83046
Summary: In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles. We find several possibilities, depending on the choice of the gauge fixing term. Amongst these, two solutions with good massless limit are found. The request of the absence of tachyons, alone, does not isolate the Fierz-Pauli case: several examples of massive theories, which may or may not include the Fierz-Pauli mass term, are given. On the other hand, the Fierz-Pauli theory can be uniquely identified by means of a symmetry: it turns out the the Fierz-Pauli massive gravity is the only element of the cohomology of a BRS operator.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 83C45 | Quantization of the gravitational field |
| 55S05 | Primary cohomology operations in algebraic topology |
| 83A05 | Special relativity |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
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