Functional evolution of scalar fields in bounded one-dimensional regions
  We discuss the unitarity of the quantum evolution between arbitrary Cauchy surfaces of a 1+1 dimensional free scalar field defined on a bounded spatial region and subject to several types of boundary conditions including Dirichlet, Neumann and Robin. 
J. Fernando G. Barbero, Juan Margalef-Bentabol and Eduardo J. S.   Villase\~nor
gr-qc hep-th