General geometric operators in all dimensional loop quantum gravity

Abstract

Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum, which play the role of building block for the spatial geometry. The first regularization method is a generalization of the regularization of the length operator in standard $(1+3)$-dimensional loop quantum gravity, while the second method is a natural extension of those for standard (D-1)-area and D-volume operators. Two versions of general geometric operators to measure arbitrary $m$-areas are constructed, and their properties are discussed and compared. They serve as valuable candidates to study the quantum geometry in arbitrary dimensions.

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• Superposition type coherent states in all dimensional loop quantum gravity
• Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The effective dynamics of weak coupling loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology