Showing papers by "Jerzy Lewandowski published in 1995"
TL;DR: In this article, a quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphicism constraint is solved and the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions.
Abstract: 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.
707 citations
TL;DR: In this paper, a general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces, then applied to gauge theories to carry out integration over the non-linear, infinite-dimensional spaces of connections modulo gauge transformations.
Abstract: A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non‐linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular, prior knowledge of projective techniques is not assumed.
425 citations
TL;DR: In this article, the projective limit of a projective family of compact Hausdorff manifolds, labelled by graphs, is considered, and the notion of differential geometry is introduced.
331 citations
TL;DR: In this article, a solution of the diffeomorphism constraints is found, equipped with an inner product that is shown to satisfy the physical reality conditions, which provides, in particular, a quantization of the Husain-Kuchař model.
Abstract: Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. 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 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 combined in an appropriate fashion with a coherent state transform to incorporate complex connections.
16 citations
01 Jan 1995
TL;DR: In this article, the authors present a pedagogical account of the non-linearity of the space of histories of physical histories and suggest an avenue for its resolution. But they do not address the problem of nonlinearity in quantum field theory.
Abstract: In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these {\it kinematical} non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.
1 citations