Quantization of diffeomorphism invariant theories of connections is studied and the quantum
diffeomorphism constraint is solved. The space of solutions is equipped with an inner …

In a quantum mechanical treatment of gauge theories (including general relativity), one is
led to consider a certain completion AG of the space AG of guage equivalent connections …

The algebraic form of the Hamiltonian or Hamiltonian constraint of various (field) theories
simplifies considerably if one uses certain complex-valued phase space variables. We …

The Segal–Bargmann transform plays an important role in quantum theories of linear fields.
Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie …

The ADM approach to canonical general relativity combined with Dirac's method of
quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of …

In this article we summarize and describe the recently found transforms for theories of
connections modulo gauge transformations associated with compact gauge groups …

The loop transform in quantum gauge field theory can be recognized as the Fourier
transform (or characteristic functional) of a measure on the space of generalized …

Since the gauge group underlying (2+ 1)-dimensional general relativity is non-compact,
certain difficulties arise in the passage from the connection to the loop representations. It is …

This is a summary of the lectures presented at the Xth Brazilian school on cosmology and
gravitation. The style of the text is that of a lightly written descriptive summary of ideas with …

Quantisation is a highly successful heuristic tool for constructing a quantum theory out of a
classical theory---even though it is typically accepted that the classical is derivative on the …