arXiv subjects
Publications and source records attributed to P. Presnajder.
We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We explicitely show that the model is finite and the UV-regularization automatically takes place.
Heavy quark potential in the continuum theory at finite temperature is calculated in different phases by using the Polyakov loop as the order parameter. We find the linearly rising potential in the confinement phase, the Debye screened potential in the deconfinement phase and the perturbative $r^{-2}$ dependence at very high temperatures. Within the approximation used in this paper we report an evidence of the first order phase transition accompanied by the $SU(2)$ symmetry restoration at very high temperatures in the static three dimensional theory.
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.