Quantization of the Diffeomorphism Field Through Effective Gravity Constraints

Salvatore Quaid

Two-dimensional effective gravity can be shown to generate a Hamiltonian constraint. Utilizing the commutation relation of the phase-space variables and the Hamiltonian constraint, the diffeomorphism field can be written in terms of a mode expansion. It will be demonstrated that the original two-dimensional anomalous contribution to gravity cancels, and the diffeomorphism field is shown to only depend on terms from the new contribution. In terms of annihilation/creation operators, it will be shown that the diffeomorphism field takes the form of a number operator with a Fourier space variable dependence. A naive integration over the Fourier space variable finds an infinite contribution to the diffeomorphism field. However, using results from the wave analysis of the Minkowski gauge of Thomas-Whithead gravity, non-infinite solutions can be found. A similar analysis is done in a Cartesian coordinate system, where the Hamiltonian constraint is no longer recovered. The talk will begin with a brief review of constraint analysis and canonical quantization.