A ghost-parity-preserving perturbation theory, Z2PT, reproduces old-fashioned perturbation theory for real amplitudes through third order and, when the parity-preserving interaction vanishes, through fourth order, with contact-term differences that leave local primitive UV divergences unchanged.
Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
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abstract
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.
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Superselected ghost theory: perturbation theory
A ghost-parity-preserving perturbation theory, Z2PT, reproduces old-fashioned perturbation theory for real amplitudes through third order and, when the parity-preserving interaction vanishes, through fourth order, with contact-term differences that leave local primitive UV divergences unchanged.