English

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