Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-02-23
Phys.Rev. D70 (2004) 025001; Erratum-ibid. D71 (2005) 049901
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, 4 figures
Scientific paper
10.1103/PhysRevD.70.025001
It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory.
Bender Carl M.
Brody Dorje C.
Jones Hugh F.
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