Boundary Hilbert spaces and trace operators

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.

13 pages. Accepted for publication in Classical and Quantum Gravity

References in corpus (5)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Isolated and dynamical horizons and their applications
• Quantum Darwinism, Classical Reality, and the Randomness of Quantum Jumps
• Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach
• Quantization of scalar fields coupled to point-masses

Cited by in corpus (5)

• Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type
• Ground State for the Klein-Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions
• Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states
• Edge observables of the Maxwell-Chern-Simons theory
• The cost of building a wall for a fermion