Approaches to quantum gravity of Bergmann and the Syracuse School

Already from the onset in 1949 of Peter G. Bergmann's efforts to construct a quantum theory of gravity he posited the underlying general covariance of Einstein's theory as a foundational principle. This led him and his collaborators to a constrained Hamiltonian procedure that is now known as the Rosenfeld-Bergmann-Dirac method. It was he who recognized, beginning in 1962, that Dirac's decomposition of infinitesimal general coordinate transformations led to a compulsory metric field dependence of the underlying gauge symmetry group. The consequent identification of equivalence classes and associated invariant Poisson bracket algebras of the true degrees of freedom of general relativity constitutes a conflict with the still dominant geometrodynamical approach promoted by John Archibald Wheeler