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P. Kosinski

Publications and source records attributed to P. Kosinski.

At least 37 records · Page 2Linked to original sources
arXiv2004

Quadratic integrals of motions for the systems of identical particles-quantum case

The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed.

nlin.SI↗
arXiv2003

Depurification by Lorentz boosts

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed.

quant-ph↗
arXiv2000

Quantum Deformations of Space-Time SUSY and Noncommutative Superfield Theory

We review shortly present status of quantum deformations of Poincaré and conformal supersymmetries. After recalling the $κ$-deformation of $\hbox{D=4}$ Poincaré supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over $κ$-deformed chiral superspace is proposed.

hep-th↗
arXiv2000

Local Field Theory ON $κ$-Minkowski Space, Star Products and Noncommutative Translations

We consider local field theory on $κ$-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over $κ$-Minkowski space and $κ$-deformed Fourier transform we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicite formulas for two equivalent star products describing CBH quantization of field theory on $κ$-Minkowski space. We express also via star product technique the noncommutative translations in $κ$-Minkowski space by commutative translations in standard Minkowski space.

hep-th↗
arXiv1998

Calogero model and sL(2,R) algebra

The Calogero model with external harmonic oscillator potential is discussed from sL(2,R) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are constructed and their involutiveness demonstrated. The superintegrability of the model appears to be a simple consequence of the formalism.

hep-th↗
arXiv1998

Projective representation of k-Galilei group

The projective representations of k-Galilei group G_k are found by contracting the relevant representations of k-Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G_k by vector representations of some its extension.

math.QA↗
arXiv1996

Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.

solv-int↗
arXiv1995

Galilean invariance in 2+1 dimensions

The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some detail.

hep-th↗
arXiv1995

Central potential and examples of hidden algebra structure

We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrhödinger equations. Some relativistic counterparts of these problems are also discussed.

hep-th↗