Coherent state transforms for spaces of connections

Journal article

Publication Details

Author(s): Ashtekar A, Lewandowski J, Marolf D, Mourao JM, Thiemann T
Journal: Journal of Functional Analysis
Publication year: 1996
Volume: 135
Journal issue: 2
Pages range: 519-551
ISSN: 0022-1236


The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group G with its normalized Haar measure mu(H), the Hall transform is an isometric isomorphism hem L(2)(G, mu(H)) to H(G(C)) boolean AND L(2)(G(C), v), where G(C) the complexification of G, H(G(C)) the space of holomorphic functions on G(C), and v an appropriate heat-kernel measure on G(C). We extend the Hall transform to the infinite dimensional context of non-Abelian gauge theories by replacing the Lie group G by (a certain extension of) the space A/g of connections module gauge transformations. The resulting ''coherent state transform'' provides a holomorphic representation of the holonomy C* algebra of real gauge fields. This representation is expected to play a key role in a non-perturbative, canonical approach to quantum gravity in 4 dimensions. (C) 1996 Academic Press, Inc.

FAU Authors / FAU Editors

Lewandowski, Jerzy
Chair for Theoretical Physics III (Quantum Gravity)
Mourao, José Manuel Prof. Dr.
Chair for Theoretical Physics III (Quantum Gravity)
Thiemann, Thomas Prof. Dr.
Chair for Theoretical Physics III (Quantum Gravity)

How to cite

Ashtekar, A., Lewandowski, J., Marolf, D., Mourao, J.M., & Thiemann, T. (1996). Coherent state transforms for spaces of connections. Journal of Functional Analysis, 135(2), 519-551.

Ashtekar, Abhay, et al. "Coherent state transforms for spaces of connections." Journal of Functional Analysis 135.2 (1996): 519-551.


Last updated on 2018-10-08 at 19:53