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

By C. Bender, Dorje C. Brody, H. Jones. 2004

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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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Citations in the corpus

Observation of parity–time symmetry in optics (2010, background): “Even though the Hermiticity of quantum observables was never in doubt, such concepts have motivated discussions on several fronts in physics, including quantum field theorie”