Uniqueness of measures in loop quantum cosmology

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4931397· OSTI ID:22479602

Hanusch, Maximilian ^[1]

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1. Mathematics Department, University of Paderborn, Paderborn (Germany)

In Ashtekar and Campiglia [Classical Quantum Gravity 29, 242001 (2012)], residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations with respect to the extended ℝ-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space ℝ{sub Bohr} as well as on the Fleischhack one (ℝ⊔ℝ{sub Bohr}). Thus, in both situations, the same condition singles out the standard kinematical Hilbert space of LQC.

• OSTI ID: 22479602
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
HILBERT SPACE
QUANTUM COSMOLOGY
QUANTUM GRAVITY
UNITARITY