Positronium Spectroscopy in a Magnetic Field

Hyperfine spectroscopy of positronium formed in the presence of a static magnetic field is considered. Generalising the situation hitherto developed in the literature, the magnetic field is not assumed to be parallel to the momentum of incoming polarised positrons, while the possibility of electron polarisation is also included in the analysis. The results are of application to high sensitivity positron polarimeters used in current $\beta$ decay experiments.Comment: 17 pages (LateX file; no extra macros needed

Noncommuting Coordinates and Magnetic Monopoles

The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been restricted to the lowest energy level. Quantum corrections are found to previous results by Frenkel and Pereira based on quantizing the Dirac brackets of the classical theory. For two different potentials, the modified harmonic oscillator potential and the modified Coulomb potential, we also calculate the commutators for a projection to a fixed energy level.Comment: 8 pages, Late

Noncommutative Spherically Symmetric Spaces

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.Comment: 9 pages, revtex, matches Phys.Rev.D versio

Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter

A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a quantum realization of the conformal algebra for physical quantum states of the fields naturally constrains the cosmological constant to take values in a well determined and mostly discrete spectrum. Furthermore the contribution of the quantum fluctuations of the single dynamical degree of freedom in the gravitational sector, namely the conformal mode, to the cosmological constant is negative, in contrast to the positive contributions of the quantum fluctuations of the matter fields, possibly opening an avenue towards addressing the cosmological constant problem in a more general context.Comment: 23 page

Superconductivity and Electric Fields: A Relativistic Extension of BCS Superconductivity

The effects of static electric fields on the superconducting state are studied within a relativistic extension of the BCS theory of superconductivity.Comment: To appear in the Proceedings of the Fourth International Workshop on Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou (Republic of Benin) (World Scientific, Singapore, 2006), 1+17 pages, no figure