Topological Quantum Field Theory Seminar   RSS

23/01/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building
, 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.


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

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Current organizers: José MourãoRoger Picken, Marko Stošić


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.