Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity

Abstract

A generally covariant U(1)3 gauge theory describing the GN→0 limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we the study boundary conditions and asymptotic symmetries of the U(1)3 model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that the non-Abelian part of the SU(2) Gauss constraint, which is absent in the U(1)3 model, plays a crucial role in obtaining boost and rotation generators.