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arXiv · hep-th/0501180

PT-Symmetric Quantum Electrodynamics

Carl M. Bender·Ines Cavero-Pelaez·Kimball A. Milton·K. V. Shajesh
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Abstract

The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^μ$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $ϕ$ has a cubic self-interaction of the form $iϕ^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.

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Carl M. Bender, Ines Cavero-Pelaez, Kimball A. Milton, K. V. Shajesh. 2005-01-21. PT-Symmetric Quantum Electrodynamics. https://doi.org/10.1016/j.physletb.2005.03.032

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