QUANTIZATION BY NON-ABELIAN PROMEASURES

A new method is proposed for the non-perturbative quantization of certain nonlinear field theories (group-bundle theories), based on a generalization of the idea of a promeasure from vector spaces to infinite-dimensional Lie groups. The quantum theory is not automatically finite, but there is a natural way of imposing a momentum cut-off, leading to the possibility of renormalization. The method relies on the geometrical structure of the classical theory and so may provide clues for the quantization of gravity.