The Hamiltonians of Linear Quantum Fields: I. Existence Theory
High Energy Physics - Theory
2007-05-23 v3 General Relativity and Quantum Cosmology
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9908011,
title = {The Hamiltonians of Linear Quantum Fields: I. Existence Theory},
author = {Adam D. Helfer},
journal= {arXiv preprint arXiv:hep-th/9908011},
year = {2007}
}
Comments
30 pages, Latex2e with AMS packages