Abstract:
An ultraviolet finite theory of quantum gravity has been elusive. Gravity coupled to higher spin fields, described by the Vasiliev model, is one candidate for a finite theory of gravity but it has no known action principle. This thesis presents a light-cone method to determine interaction vertices, and hence Lagrangians, by demanding closure of the symmetry algebra of the background spacetime. In particular, we discuss the derivation of cubic interaction vertices for massless fields of arbitrary spin and quartic interaction vertices for spin-1 fields in four-dimensional Minkowski spacetime. The requirement of antisymmetric constants for odd spin fields is noted at the cubic level. It is observed that, at the quartic level, algebra closure forces the Jacobi identity onto these constants and dictates the existence of a gauge group. Some of the work being done to extend this method to higher spin fields in AdS4 is included.
In addition, this thesis describes certain features of the pure gravity Hamiltonian that may point to hidden symmetries in the theory. We find that the Hamiltonian can be expressed as a quadratic form and determine its residual reparametrization invariances. The transformation properties of the quadratic form structure are studied.
