  Peter Bergmann and his students embarked in 1949 on a mainly canonical
quantization program whose aim was to take into account the underlying
four-dimensional diffeomorphism symmetry in the transition from a Lagrangian to
a Hamiltonian formulation of Einstein's theory. They argued that even though
one seemed to destroy the full covariance through the focus on a temporal
foliation of spacetime, this loss was illusory. Early on they convinced
themselves that only the construction of classical invariants could adequately
reflect the fully relativistic absence of physical meaning of spacetime
coordinates. Efforts were made by Bergmann students Newman and Janis to
construct these classical invariants. Then in the late 1950's Bergmann and
Komar proposed a comprehensive program in which classical invariants could be
constructed using the spacetime geometry itself to fix intrinsic spacetime
landmarks. At roughly the same time Dirac formulated a new criterion for
identifying initial phase space variables, one of whose consequences was that
Bergmann himself abandoned the gravitational lapse and shift as canonical
variables. Furthermore, Bergmann in 1962 interpreted the Dirac formalism as
altering the very nature of diffeomorphism symmetry. One class of infinitesimal
diffeomorphism was to be understood as depending on the perpendicular to the
given temporal foliation. Thus even within the Bergmann school program the
preservation of the full four-dimensional symmetry in the Hamiltonian program
became problematic. Indeed, the ADM and associated Wheeler-DeWitt program that
gained and has retained prominence since this time abandoned the full symmetry.
There do remain dissenters - raising the question whether the field of quantum
gravity has witnessed a Renaissance in the ensuing decades - or might the full
four-dimensional symmetry yet be reborn?
