This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the establishment of a procedure for quantizing in curved spaces; the first expressions for the Hamiltonian of general relativity; recognition of the existence and importance of constraints (i.e. the generators of infinitesimal coordinate transformations); a focus on the problem of observables (and the realisation of conceptual implications in defining these for generally relativistic theories), and a (template of a) method for quantizing the theory. Although it commenced relatively early, the canonical approach was slow in its subsequent development. This had two sources: (1) it required the introduction of tools and concepts from outside of quantum gravity proper (namely, the constraint machinery and the parameter formalism); (2) by its very nature, it is highly rigorous in a conceptual sense, demanding lots of groundwork to be established, in terms of the structure of physical observables, before the actual issue of quantization can even be considered. Work was further complicated by the fact that these two sources of difficulty happened to be entangled. Particular emphasis is placed on the parameter formalism of Paul Weiss.
GENERALIZED QUANTIZATION PRINCIPLE IN CANONICAL QUANTUM GRAVITY AND APPLICATION TO QUANTUM COSMOLOGY