Gravitons and loops

The recently proposed loop representation is used to quantize linearized general relativity. The Fock space of graviton states and its associated algebra of observables are represented in terms of functionals of loops. The "reality conditions" are realized by an inner product that is chiral asymmetric, resulting in a chiral-asymmetric ordering for the Hamiltonian, and, in an asymmetric description of the left- and right-handed gravitons. The formalism depends on an arbitrary "averaging" function that controls certain divergences, but does not appear in the final physical quantities. In spite of these somewhat unusual features, the loop quantization presented here is completely equivalent to the standard quantization of linearized gravity.