29 citations · 114 across the 15 of their papers we have counts for
16 papers
Quantized Bertrand models on two-dimensional spaces of constant curvature
Agnieszka Martens
Discussed are Bertrand systems on two-dimensional spaces of constant curvature, i.e. sphere and pseudosphere (Lobachevsky space). These models often involve applying quantization t…
Quantized Kepler-Coulomb dynamical models on two-dimensional constant curvature spaces
Agnieszka Martens
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaki…
Quantized Mechanics of Affinely-Rigid Bodies
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Barbara Gołubowska +2
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schrödinger formulatio…
Why must we work in the phase space?
J. J. Sławianowski, F. E. Schroeck, A. Martens
We are going to prove that the phase-space description is fundamental both in the classical and quantum physics. It is shown that many problems in statistical mechanics, quantum me…
Space-time as a structured relativistic continuum
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Barbara Gołubowska +2
It is well known that there are various models of gravitation: the metrical Hilbert-Einstein theory, a wide class of intrinsically Lorentz-invariant tetrad theories (of course, gen…
Generalized Weyl-Wigner-Moyal Formalism and Topological Groups
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this forma…
Affine Bodies Revisited. Constraints, Symmetry, Analytical Methods and Some Perspectives
J. J. Sławianowski, B. Gołubowska, E. E. Rożko +3
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension . O…
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
Jan Jerzy Sławianowski, Vasyl Kovalchuk, Agnieszka Martens +2
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possibl…
Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the…
Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
We use the mathematical structure of group algebras and -algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including al…
Quasiclassical and Quantum Systems of Angular Momentum. Part III. Group Algebra of , Quantum Angular Momentum and Quasiclassical Asymptotics
J. J. Sławianowski, V. Kovalchuk, A. Martens +2
This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation…
Affinely-rigid body and oscillatory dynamical models on GL(2,R)
Agnieszka Martens, Jan J. Sławianowski
Discussed is a model of the two-dimensional affinely-rigid body with the double dynamical isotropy. We investigate the systems with potential energies for which the variables can b…
Quantized excitations of internal affine modes and their influence on Raman spectra
J. J. Sławianowski, V. Kovalchuk, B. Gołubowska +2
Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on som…
Dynamical systems with internal degrees of freedom in non-Euclidean spaces
J. J. Sławianowski, V. Kovalchuk, B. Gołubowska +2
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom w…
Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models
J. J. Sławianowski, V. Kovalchuk, A. Sławianowska +4
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schrödinger quantization and reduce e…
Affine symmetry in mechanics of collective and internal modes. Part I. Classical models
J. J. Sławianowski, V. Kovalchuk, A. Sławianowska +4
Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempt…