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The inverse loop transform

Authors
  • Thiemann, Thomas
Type
Published Article
Publication Date
Jan 19, 1996
Submission Date
Jan 19, 1996
Identifiers
DOI: 10.1063/1.532344
arXiv ID: hep-th/9601105
Source
arXiv
License
Unknown
External links

Abstract

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 connections modulo gauge transformations. Since this space is a compact Hausdorff space, conversely, we know from the Riesz-Markov theorem that every positive linear functional on the space of continuous functions thereon qualifies as the loop transform of a regular Borel measure on the moduli space. In the present article we show how one can compute the finite joint distributions of a given characteristic functional, that is, we derive the inverse loop transform.

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