Self-adjoint time operator is the rule for finite-dimensional bounded discrete Hamiltonians

Abstract

Pauli’s theorem historically forbade the existence of operators canonically conjugate to a semibounded and discrete Hamiltonian. In recent years, this was disproven, and as a counterexample, it was shown that for every infinite-dimensional semibounded discrete Hamiltonian with some growth condition and constant degeneracy, there exists a characteristic self-adjoint operator canonically conjugate to it. In this paper, we extend it to the finite-dimensional case, and show that there always exists a characteristic self-adjoint time operator canonically conjugate to every finite-dimensional bounded discrete Hamiltonian.