Complex extension of quantum mechanics

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.     

LIGHT AND pH INDUCED CHANGES IN THE SURFACE PRESSURE-AREA ISOTHERMS OF BACTERIORHODOPSIN

Abstract— Pressure-area isotherms of monolayers of purple membrane fragments were measured at an air-water interface. The pH of the aqueous phase was varied from 2 to 10. Over the pH range 5 to 9 the area/molecule of bacteriorhodopsin was constant and illumination of the film had no effect on the isotherms.
At pH's more acid than 5 and more alkaline than 9, there were large decreases in area/molecule. Under these conditions of extreme pH the monolayer was very sensitive to light. Illumination resulted in irreversible increases in area/molecule.     

SPECTRAL CHANGES IN CHLOROPLASTS DURING AGING

The spectral properties of photosynthetic and accessory pigments of chloroplasts can change significantly over the course of an experiment which may last a couple of hours. As chloroplasts age at room temperature, there are decreases in absorbance at 708, 678, 510, 484, 465 and 432 nm. Chlorophylls absorbing at long wavelength (708 nm) and carotenoids (510 nm) are most sensitive to the aging process. The decrease in absorbance at 510 nm could indicate that aging results in a decrease in electrical potential across the thylakoid membrane.     

Scalar quantum field theory with a complex cubic interaction

In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.