Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9861354 | Physics Letters B | 2005 | 8 Pages |
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 Aμ 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 Ï has a cubic self-interaction of the form iÏ3. 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 Letter 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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Nuclear and High Energy Physics
Authors
Carl M. Bender, Ines Cavero-Pelaez, Kimball A. Milton, K.V. Shajesh,