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arXiv · hep-th/9908011

The Hamiltonians of Linear Quantum Fields: I. Existence Theory

Adam D. Helfer
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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.

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Adam D. Helfer. 2003-08-13. The Hamiltonians of Linear Quantum Fields: I. Existence Theory. https://arxiv.org/abs/hep-th/9908011

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