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Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction

Carl M. Bender·Dorje C. Brody·Hugh F. Jones
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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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Carl M. Bender, Dorje C. Brody, Hugh F. Jones. 2004-02-23. Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction. https://doi.org/10.1103/physrevd.70.025001%2010.1103%2Fphysrevd.71.049901

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