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Cezary J. Walczyk

Publications and source records attributed to Cezary J. Walczyk.

13 recordsLinked to original sources
arXiv2019

The spinning particles -- classical description

The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes non-linear. Nevertheless the equations of motion are analyzed in details and solved numerically. In either case the trajectories are ilustrated and their properties are disussed. There is also discussion of possible physical quantities associated with the spinning motions. Among others: the size of particles and their gyromagnetic ratios. Finally, some possible, speculative explanations of the properties of the Universe are proposed: the origin and nature of dark matter and lack of the equilibrium bettween mater and anti-matter.

physics.class-ph↗
arXiv2019

Determination of topological properties of thin samples by the van der Pauw method

We solve the problem of determining basic topological properties of flat samples by performing measurements on their outer edge. The global maximum of four probe resistances shows a characteristic behaviour, which is dependent on the genus (i.e., the number of holes) of the domain. An extension of the van der Pauw method on domains having zero, one, or two holes is presented and discussed. A possibility of measuring topological properties of condensed matter is demonstrated. Experimental results for triply connected domains are presented and explained by continuous symmetry breaking caused by the presence of two holes. The results are consistent with the topological theorem of Hurwitz on the number of automorphisms of Riemann surfaces.

physics.class-ph↗
arXiv2018

Improving the accuracy of the fast inverse square root algorithm

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or similar computational cost. The main idea of our work consists in modifying the Newton-Raphson method and demanding that the maximal error is as small as possible. Such modification is possible when the distribution of Newton-Raphson corrections is not symmetric (e.g., if they are non-positive functions).

math.NA↗
arXiv2014

Kerr black hole in canonically deformed space-time

We investigate the Kerr black hole defined on canonically deformed space-time. Particulary, we find the corresponding event horizon, the ergosphere, the temperature and the entropy of such deformed object.

hep-th↗
arXiv2013

Cohomological resolutions for anomalous Lie constraints

It is shown that the BRST resolution of the spaces of physical states of the systems with anomalies can be consistently defined. The appropriate anomalous complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of anomaly operator without any modifications of the "matter" sector. The cohomologies of the anomalous complex for the case of constarints constituting a centrally extended simple Lie algebra of compact type are calculated and analyzed in details within the framework of Hodge - deRham - Kaehler theory: the vanishing theorem of the relative cohomologies is proved and the absolute cohomologies are reconstructed.

math-ph↗
arXiv2009

Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space

The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of particle is generated. We also indicate, that in the case of spatial coordinates commuting in Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.

math-ph↗
arXiv2007

High spin particles with spin-mass coupling II

The classical and quantum model of high spin particles with spin-mass coupling is presented in this paper. The mass spectrum of the model is symmetric with respect to particle-antiparticle exchange. The quantum model contains elementary particles and the cluster states generating infinite degeneracy of the mass spectrum.

hep-th↗
arXiv2007

High spin particles with spin-mass coupling

The classical and quantum model of high spin particles is proposed and analyzed in this paper. The covariant quantization leads to the spectrum of the particles with the masses correlated with their spins. The particles (and anti-particles) appear to be orphaned as their potential anti-particle partners are of different mass.

hep-th↗
arXiv2006

Anomalus BRST Complexes for Non-Critical Massive Strings

It is shown that the BRST resolution of the spaces of physical states of non-critical (anomalus) massive string models can be consistently defined. The appropriate anomalus complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of curvature operator and additional Gupta-Bleuler like conditions without any modifications of the matter sector. The cohomologies of the polarized anomalus complex are calculated and analyzed in details.

hep-th↗