José Mourão

Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

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 product that is shown to satisfy the physical reality conditions. This provides, in particular, a quantization of the Husain–Kuchař model. The main results also pave the way to quantization of other diffeomorphism invariant theories such as general relativity. In the Riemannian case (i.e., signature ++++), the approach appears to contain all the necessary ingredients already. In the Lorentzian case, it will have to be combined in an appropriate fashion with a coherent state transform to incorporate complex connections.

On the support of the Ashtekar-Lewandowski measure

AbstractWe show that the Ashtekar-Isham extension

Quantum gravity and the large scale structure of the universe

\overline {A/G}

SU(N) Quantum Yang–Mills theory in two dimensions: A complete solution

of the configuration space of Yang-Mills theories

Coherent state transforms and vector bundles on elliptic curves

A/G

Physical properties of quantum field theory measures

is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that