Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-01-21
Phys.Lett.B613:97-104,2005
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, no figures, revtex4
Scientific paper
10.1016/j.physletb.2005.03.032
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 $A^\mu$ 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 $\phi$ has a cubic self-interaction of the form $i\phi^3$. 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.
Bender Carl M.
Cavero-Pelaez Ines
Milton Kimball A.
Shajesh K. V.
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