Sahlmann H, Seeger R (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 101
Journal Issue: 10
DOI: 10.1103/PhysRevD.101.106018
An important challenge in loop quantum gravity is to find semiclassical states-states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in loop quantum gravity are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. We reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra. We then define and investigate a new class of states on this algebra which behave as quasifree states on the momentum variables. Using a general result on representations of the holonomy-flux algebra, we define analogous representations also in the case of non-Abelian compact structure groups. For the case of SU(2), we study an explicit example of such a representation and the consequences for quantum geometry. This kind of state, with Gaussian fluctuations in the spatial geometry, seems well suited to investigate problems related to structure formation in cosmology.
APA:
Sahlmann, H., & Seeger, R. (2020). Towards Gaussian states for loop quantum gravity. Physical Review D, 101(10). https://dx.doi.org/10.1103/PhysRevD.101.106018
MLA:
Sahlmann, Hanno, and Robert Seeger. "Towards Gaussian states for loop quantum gravity." Physical Review D 101.10 (2020).
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