JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 52 / Issue 1 / ARTICLES / General Relativity and Gravitation

J. Math. Phys. 52, 012503 (2011); http://dx.doi.org/10.1063/1.3525706 (14 pages)

When do measures on the space of connections support the triad operators of loop quantum gravity?

Hanno Sahlmann

Asia Pacific Center for Theoretical Physics, Pohang, Korea

View MapView Map

(Received 17 June 2010; accepted 18 November 2010; published online 20 January 2011)

In this work we investigate the question under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of “no-go theorems” asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider, play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non-Abelian gauge theories.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MEASURES ON THE SPACE OF GENERALIZED CONNECTIONS
  3. ADMISSIBILITY
  4. ADMISSIBILITY IN THE U(1) CASE
    1. Diffeomorphism invariant measures
    2. Factorizing measures
    3. Varadarajan measures
  5. DISCUSSION

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

group theory, Hilbert spaces, quantum gravity, quantum theory

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3525706

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to citing articles, you need to log in.


Figures (5)

Access to article objects (figures, tables, multimedia) requires a subscription; log in to view available files.
(Access to supplementary files, where available, is free for this journal.)



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. When do measures on the space of connections support the triad operators of loop quantum gravity?
  2. The energy minimization problem for two-level dissipative quantum systems
  3. Separability of N-particle fermionic states for arbitrary partitions
  4. Fast universal quantum computation with railroad-switch local Hamiltonians
  5. Comment on “Functional determinants in higher derivative Lagrangian theories” [ J. Math. Phys. 50, 103517 (2009) ]
Go to AIP Home
Copyright © American Institute of Physics
close