Modern Physics Letters A

Noncommutative algebra in planar quantum mechanics is shown to follow from 't Hooft's recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a charged particle in a magnetic field with an oscillator potential is shown as dual description of the same phenomenon. Finally, noncommutativity in a fluid dynamical model, analogous to the lowest Landau level problem, is discussed.

The propagation of a boson particle in the Janis–Newman–Winicour–Wyman (JNWW) gravitational field is analyzed. We derive the wave function of the scalar particle, and the effective potential experienced by quantum particles. Besides, we show that the probability to find the scalar particle near the region where the naked singularity is finite. Finally, these results are proposed as a model to study the gamma ray bursts (GRBs) physics.

A systematic method developed by us to evaluate the one-loop electromagnetic self-energies of the low-lying mesons is extended to the case of the ρ-meson. The theoretical prediction of ρ⁰-ρ^± electromagnetic mass splitting is about 0.62 MeV, which is in agreement with the measurements.

Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H (η) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type , (γ ≠ 2/3), in the sech FRW adiabatic index soliton.

We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau–Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a Pöschl–Teller potential of the trigonometric type. Some comparisons with Barut–Girardello and Klauder–Perelomov methods are noted.

In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL(2,R) WZNW model.

We cast the flat space theory of a scalar field in generally covariant form by introducing an auxiliary field λ. The resulting theory is couched in terms of an action integral S, and all the fields (the scalar, the space–time metric, and λ) are dynamical in the sense of being varied freely in S. Conservation of energy–momentum emerges as a formal consequence of diffeomorphism invariance, in close analogy with the situation in ordinary general relativity.