Duals of U(N) LGT with staggered fermions

Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions. Applications related to the finite temperature/density QCD are discussed.Comment: 8 pages, Proceedings for the 35th International Symposium on Lattice Field Theory (Lattice 2017

Description of texts of auxiliary programs for processing video information. Part 2: SUODH program of automated separation of quasihomogeneous formations

The algorithm, block diagram, complete text, and instructions are given for the use of a computer program to separate formations whose spectral characteristics are constant on the average. The initial material for operating the computer program presented is video information in a standard color-superposition format

Fresh look on triality

Investigating the $Z_3$ symmetry in Quantum Chromodynamics (QCD) we show that full QCD with a vacuum of vanishing baryonic number does not lead to metastable phases. Rather in QCD with dynamical fermions, the degeneracy of $Z_3$ phases manifests itself in observables without open triality.Comment: 9 pages, 0 figures, latex, IK-TUW-Preprint 930840

ARPES on HTSC: simplicity vs. complexity

A notable role in understanding of microscopic electronic properties of high temperature superconductors (HTSC) belongs to angle resolved photoemission spectroscopy (ARPES). This technique supplies a direct window into reciprocal space of solids: the momentum-energy space where quasiparticles (the electrons dressed in clouds of interactions) dwell. Any interaction in the electronic system, e.g. superconducting pairing, leads to modification of the quasi-particle spectrum--to redistribution of the spectral weight over the momentum-energy space probed by ARPES. A continued development of the technique had an effect that the picture seen through the ARPES window became clearer and sharper until the complexity of the electronic band structure of the cuprates had been resolved. Now, in an optimal for superconductivity doping range, the cuprates much resemble a normal metal with well predicted electronic structure, though with rather strong electron-electron interaction. This principal disentanglement of the complex physics from complex structure reduced the mystery of HTSC to a tangible problem of interaction responsible for quasi-particle formation. Here we present a short overview of resent ARPES results, which, we believe, denote a way to resolve the HTSC puzzle.Comment: A review written for a special issue of FN

Compatibility of Gauss maps with metrics

We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold $M^m$ into the sphere $S^m$ to be the Gauss map of an isometric immersion $u:M^m \to R^n$, $n=m+1$. We briefly discuss the case of general $n$ as wellComment: 14 pages, no figure