Boundary Hilbert spaces and quantisation of field-particle composite systems

Benito Juárez-Aubry (ICN-UNAM)

Resumen: We show how to associate natural boundary Hilbert spaces to the quantisation of classical systems in bounded regions, that can be understood as composite boundary-bulk systems. As an example, we will show in detail how one can Fock quantise a linear field-particle interacting system consisting of a string with two point masses attached at the ends. We shall see that, although the quantised system cannot be immediately decomposed as a tensor product of 'masses' and 'string' Hilbert spaces, there is a natural Hilbert space that can be associated to the boundary with the aid of so-called trace operators from PDE theory.