Boundary Hilbert spaces and trace operators Articles uri icon

publication date

  • March 2017

start page

  • 1

end page

  • 12

issue

  • 9 (095005)

volume

  • 34

International Standard Serial Number (ISSN)

  • 0264-9381

Electronic International Standard Serial Number (EISSN)

  • 1361-6382

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 PDEs 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.

keywords

  • quantum field theory; boundary hilbert spaces; second quantization functor; trace operators; fock quantization