Physics
Scientific paper
Feb 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tmgm.meet..221k&link_type=abstract
The Tenth Marcel Grossmann Meeting. Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Rio
Physics
Scientific paper
Affine quantum gravity is based on a 3+1 split of spacetime in Einstein's theory, and gets its name from its use of affine commutation relations. Unlike canonical commutation relations, affine commutation relations involve self-adjoint kinematical field operators that preserve strict positivity of the 3 × 3 metric tensor. Gravitational physics enters through constraints, and because the quantum version of gravitational constraints are partially second class, we use the projection operator method to enforce them since this method treats all kinds of constraints on an equal basis. Enforcing the constraints fully requires fine tuning of the basic operator representation along with a proper choice of any counterterms. When perturbatively nonrenormalizable theories are understood as due to hard-core interactions, it is recognized that traditional counterterms are generally incorrect and are to be replaced by alternative counterterms. To assist in this program, functional methods such as coherent states and functional integrals with continuous-time regularization provide an especially useful framework for analysis.
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