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José Velhinho, Univ. Beira Interior and CENTRA

Representations of holonomy algebras and shadow states

It has been argued that the Ashtekar-Lewandowski
representation of the
Ashtekar-Isham holonomy algebra is fundamental, in the sense that any
other
representation can be obtained by a suitable limit procedure.
We propose to clarify that statement, providing, in particular, a
canonical way
of mapping GNS states to a family of vectors of the Ashtekar-Lewandowski
Hilbert space. The so-called family of

*shadow states*thus obtained converges, as states of the algebra, to the original GNS state.#### References

- M. Varadarajan, Phys. Rev D. 64 , 104003 (2001); gr-qc/0104051
- J.M. Velhinho, Commun. Math. Phys. 227, 541 (2002); math-ph/0107002
- A. Ashtekar and J. Lewandowski, Class. Quant. Grav. 18, L117 (2001); gr-qc/0107043
- T. Thiemann, gr-qc/0206037
- H. Sahlmann, gr-qc/0207112
- A. Ashtekar, J. Lewandowski and H. Sahlmann, gr-qc/0211012