Modern Physics Letters A

Using the loop variable formalism as applied to a sigma model in curved target space, we give a systematic method for writing down gauge and generally covariant equations of motion for the modes of the free open string in curved space. The equations are obtained by covariantizing the flat space equation and then demanding gauge invariance, which introduces additional curvature couplings. As an illustration of the procedure, the spin-two case is worked out explicitly.

New relations between QCD Borel sum rules for masses of Σ⁰ and Λ hyperons are constructed. It is shown that starting from the sum rule for the Σ⁰ hyperon mass it is straightforward to obtain the corresponding sum rule for the Λ hyperon mass and vice versa.

A covariant symplectic structure can be identified, in general, starting from conservation laws connected to generic Hamiltonian invariants constructed from covariant vectors, bivectors and tensors. This feature leads to both holonomic and anholonomic formulations of Hamilton equations and Poisson brackets and it seems a deep link common to all interactions including gravity. A key role in the approach is played by affine connections instead of metric.

Noncommutative corrections to the MIC–Kepler system (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and spherical coordinates. In the framework of perturbation theory we were able to derive noncommutative corrections to the MIC–Kepler spectrum. We also found a nontrivial contribution to the linear Stark effect which did not exist in the standard hydrogen model.

We study how the noncommutative spacetime affects inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit k-dependent power spectrum up to first order in slow-roll parameters ε₁, δ₁ including the noncommutative parameter μ. In order to test the role of μ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and the slowly varying nature of μ. It turns out that the noncommutative parameter μ could be considered as a zero order slow-roll parameter and the noncommutative spacetime effect provides a negatively large running spectral index.

The extreme Reissner–Nordström black holes have zero surface gravity. However, a semiclassical analysis seems to be ill-defined for these objects and apparently no notion of temperature exists for them. It is conjectured that these properties may be shared for all kind of black holes whose surface gravity is zero. Two examples are worked out explicitly: the scalar–tensor cold black holes and extreme black holes resulting from a gravity system coupled to a generalized Maxwell field in higher dimensions. The reasons for this anomolous behavior are discussed as well as its thermodynamics implications.