Boundary Hilbert spaces and trace operators
General Relativity and Quantum Cosmology
2017-04-03 v2
Abstract
We discuss the introduction of boundary Hilbert spaces for a class of physical systems for which it is not possible to factor their state spaces as tensor products of Hilbert spaces naturally associated to their boundaries and bulks respectively. In order to do this we make use of the so called trace operators that play a relevant role in the analysis of PDE's in bounded regions. By taking advantage of these operators and some functorial aspects of the construction of Fock spaces, we will show how to obtain quantum dynamics at the boundaries defined in appropriate Hilbert spaces associated with them.
Cite
@article{arxiv.1701.00735,
title = {Boundary Hilbert spaces and trace operators},
author = {J. Fernando G. Barbero and Benito A. Juárez-Aubry and Juan Margalef-Bentabol and Eduardo J. S. Villaseñor},
journal= {arXiv preprint arXiv:1701.00735},
year = {2017}
}
Comments
13 pages. Accepted for publication in Classical and Quantum Gravity