Licentiate Thesis Defense: Computation of constraints in bimetric theory

The Hassan-Rosen bimetric theory describes two interacting spin-2 fields, one massless and one massive. In this thesis, a complete canonical analysis of this theory is performed in the metric formulation and all constraints are computed. In particular, a secondary constraint, whose existence was in doubt, is shown to exist and explicitly evaluated, bringing the total number of constraints up to six. This, together with general covariance, is enough to eliminate the Boulware-Deser ghost and ensure that the theory propagates the appropriate seven degrees of freedom.

Since the bimetric theory is covariant, it must contain four first class constraints whose Poisson brackets form a certain algebra. According to a conjecture by Hojman, Kuchaƙ and Teitelboim, it should be possible to identify a metric from this algebra, the so called HKT metric. In this thesis, the four first class constraints of bimetric theory are identified and it is shown that their Poisson brackets indeed forms the algebra required by general covariance. However, the HKT metric turns out not to be unique, but to depend on a choice of variables. In addition, the HKT metric need not coincide with the gravitational metric.