Symmetric scalar constraint for loop quantum gravity

Sahlmann H, Lewandowski J (2015)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2015

Journal

Physical Review D - Particles, Fields, Gravitation and Cosmology American Physical Society

Book Volume: 91

Article Number: 044022

Journal Issue: 4

DOI: 10.1103/PhysRevD.91.044022

Abstract

In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints. They preserve the Hilbert space for every choice of lapse function. Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner. We show how the space of solutions of the symmetrized constraint can be defined by spectral decomposition, and the Hilbert space of physical states by subsequently fully implementing the diffeomorphism constraint. The relationship of the solutions to those resulting from a proposal for a symmetric constraint operator by Thiemann remains to be elucidated.

Authors with CRIS profile

Hanno Sahlmann Professur für Theoretische Physik

Involved external institutions

University of Warsaw / Uniwersytet Warszawski PL Poland (PL)

How to cite

APA:

Sahlmann, H., & Lewandowski, J. (2015). Symmetric scalar constraint for loop quantum gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology, 91(4). https://doi.org/10.1103/PhysRevD.91.044022

MLA:

Sahlmann, Hanno, and Jerzy Lewandowski. "Symmetric scalar constraint for loop quantum gravity." Physical Review D - Particles, Fields, Gravitation and Cosmology 91.4 (2015).

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