Coherent State Transforms for Spaces of Connections

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dc.creatorAshtekar, Abhay
dc.creatorLewandowski, Jerzy
dc.creatorMarolf, Donald
dc.creatorMourão, José
dc.creatorThiemann, Thomas
dc.date1994-12-05
dc.date.accessioned2026-07-07T03:30:34Z
dc.date.available2026-07-07T03:30:34Z
dc.descriptionThe 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 $μ_H$, the Hall transform is an isometric isomorphism from $L^2(G, μ_H)$ to ${\cal H}(G^{\Co})\cap L^2(G^{\Co}, ν)$, where $G^{\Co}$ the complexification of $G$, ${\cal H}(G^{\Co})$ the space of holomorphic functions on $G^{\Co}$, and $ν$ an appropriate heat-kernel measure on $G^{\Co}$. 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 ${\cal A}/{\cal G}$ of connections modulo gauge transformations. The resulting ``coherent state transform'' provides a holomorphic representation of the holonomy $C^\star$ 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.
dc.description38 pages, latex
dc.identifierhttps://arxiv.org/abs/gr-qc/9412014
dc.identifierhttp://arxiv.org/abs/gr-qc/9412014
dc.identifierJ.Funct.Anal. 135 (1996) 519-551
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/35566
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleCoherent State Transforms for Spaces of Connections
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