The Hamiltonians of Linear Quantum Fields: II. Classically Positive Hamiltonians

For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding quantum theories. It is shown that there is an intimate connection between boundedness-below and self-adjoint implementability. Finally, it is shown that there is a broad class of "quantum inequalities:" any timelike component of the four-momentum density operator, averaged over a compact region in curved space-time, must be bounded below.