1999/08/02 by Adam D. Helfer, Helfer, Adam D.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Applications #advanced mathematical theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9908011
30 pages, Latex2e with AMS packages
openalex publication_date 1999/08/02 · arxiv created 2003/08/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a Hadamard representation), a self-adjoint Hamiltonian for evolution along the unit timelike normal to a Cauchy surface exists only if the second fundamental form of the surface vanishes identically.