Sahlmann H, Zilker T (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 102
Journal Issue: 2
DOI: 10.1103/PhysRevD.102.026009
In this work we define a new type of flux operators on the Hilbert space of loop quantum gravity. We use them to solve an equation of the form F(A) = c Sigma in loop quantum gravity. This equation, which relates the curvature of a connection A with its canonical conjugate Sigma = *E, plays an important role for spherically symmetric isolated horizons, and, more generally, for maximally symmetric geometries and for the Kodama state. If the equation holds, the new flux operators can be interpreted as a quantization of surface holonomies from higher gauge theory. Also, they represent a kind of quantum deformation of SU(2). We investigate their properties and discuss how they can be used to define states that satisfy the isolated horizon boundary condition in the quantum theory.
APA:
Sahlmann, H., & Zilker, T. (2020). Quantum surface holonomies for loop quantum gravity and their application to black hole horizons. Physical Review D - Particles, Fields, Gravitation and Cosmology, 102(2). https://dx.doi.org/10.1103/PhysRevD.102.026009
MLA:
Sahlmann, Hanno, and Thomas Zilker. "Quantum surface holonomies for loop quantum gravity and their application to black hole horizons." Physical Review D - Particles, Fields, Gravitation and Cosmology 102.2 (2020).
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