Ines Cavero-Pelaez

PT-symmetric quantum electrodynamics

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 i φ 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 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.

Noncontact gears. II. Casimir torque between concentric corrugated cylinders for the scalar case

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for noncontact gears. To this end, we calculate the Casimir torque between two such cylinders, described by {delta}-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.

Local and global Casimir energies for a semitransparent cylindrical shell

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a λδ-function potential in a (3 + 1)-dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak coupling, through , the total energy is shown to vanish by both analytic and numerical arguments, based both on Greens-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the δ-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in , as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy and does not reflect divergences in the local energy density as the surface is approached.

Local Casimir energies for a thin spherical shell

The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness

Multiple Scattering Casimir Force Calculations: Layered and Corrugated Materials, Wedges, and Casimir-Polder Forces

\delta

Casimir energy for a dielectric cylinder

, where it has height

Surface divergences and boundary energies in the Casimir effect

h

ELECTROMAGNETIC NON-CONTACT GEARS: PRELUDE

, with the constraint

Green's dyadic approach of the self-stress on a dielectric–diamagnetic cylinder with non-uniform speed of light

h\delta=1

Lateral Casimir forces on parallel plates and concentric cylinders with corrugations

. In the limit of zero thickness, an ideal