Two-dimensional Lorentz-violating Chern-Simons-like action

We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.Comment: 10 pages, references added, version accepted to Physics Letters

Multidimensional C0C^0 transversality

In 1994, Sakai introduced the property of $C^0$ transversality for two smooth curves in a two-dimensional manifold. This property was related to various shadowing properties of dynamical systems. In this short note, we generalize this property to arbitrary continuous mappings of topological spaces into topological manifolds. We prove a sufficient condition for the $C^0$ transversality of two submanifolds of a topological manifold and a necessary condition of $C^0$ transversality for mappings of metric spaces into $\mathbb{R}^n$.Comment: 9 page