Two dimensional chiral gauge theories provide a convenient testing ground for non-perturbative regularizations since they are much simpler to simulate numerically than four dimensional ones. As in four dimensions, there are anomalies in two dimensions that have to be cancelled and anomaly free theories can have global charges that are broken by topologically non-trivial gauge fields. In this ta...

It is shown that for a non-singular conservative shift on topologically mixing Markov subshift with Doeblin Condition the only possible absolutely continuous shift-invariant measure measure. Moreover, if it not equivalent to homogeneous then of Krieger-type $\mathrm{III}_1$. A criterion equivalence measures included.

We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution in family of continuous means I^p \to I$. Some general approach to latter also given.

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient n. The phase transition is of the BerezinskyKosterlitz Thouless type, and is triggered by the liberation of Polyakov monopoles, which for n > 8 are tightly bound into pairs. In our Ha...

The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient n. The phase transition is of the BerezinskyKosterlitz Thouless type, and is triggered by the liberation of Polyakov monopoles, which for n > 8 are tightly bound into pairs. In our Ha...

Simplex meshes are simply connected meshes that are topologically dual of triangulations In a pre vious work we have introduced the simplex mesh representation for performing recognition of par tially occluded smooth objects In this paper we present a physically based approach for recovering three dimensional objects based on the geometry of simplex meshes Elastic behavior is modelled by lo cal...