Projective loop quantum gravity. II. Searching for semi-classical states

Lanery S, Thiemann T (2017)

Publication Status: Published

Publication Type: Journal article

Publication year: 2017



Book Volume: 58

Journal Issue: 5

DOI: 10.1063/1.4983133


In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. Away out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper. Published by AIP Publishing.

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How to cite


Lanery, S., & Thiemann, T. (2017). Projective loop quantum gravity. II. Searching for semi-classical states. Journal of Mathematical Physics, 58(5).


Lanery, Suzanne, and Thomas Thiemann. "Projective loop quantum gravity. II. Searching for semi-classical states." Journal of Mathematical Physics 58.5 (2017).

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