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Polish Academy of Sciences

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A. Sławianowska


Recent publications
1.  Sławianowski J.J., Kovalchuk V., Sławianowska A., Gołubowska B., Martens A., Rożko E.E., Zawistowski Z.J., Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, DOI: 10.1016/S0034-4877(05)80002-3, Vol.55, No.1, pp.1-46, 2005

Abstract:
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schroedinger quantization and reduce effectively the quantized problem from $n^2$ to $n$ degrees of freedom. Some possible applications in nuclear physics and other quantum many-body problems are suggested. Discussed is also the possibility of half-integer angular momentum in composed systems of spinless particles.

Keywords:
Collective modes, affine invariance, Schroedinger quantization, quantum many-body problem

Affiliations:
Sławianowski J.J. - IPPT PAN
Kovalchuk V. - IPPT PAN
Sławianowska A. - other affiliation
Gołubowska B. - IPPT PAN
Martens A. - IPPT PAN
Rożko E.E. - IPPT PAN
Zawistowski Z.J. - IPPT PAN
2.  Sławianowski J.J., Kovalchuk V., Sławianowska A., Gołubowska B., Martens A., Rożko E.E., Zawistowski Z.J., Affine symmetry in mechanics of collective and internal modes. Part I. Classical models, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 0034-4877, DOI: 10.1016/S0034-4877(04)80026-0, Vol.54, No.3, pp.373-427, 2004

Abstract:
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 attempts of this kind is that it is not only kinematics but also dynamics that is affinely-invariant. The relationship with the dynamics of integrable one-dimensional lattices is discussed. It is shown that affinely-invariant geodetic models may encode the dynamics of something like elastic vibrations.

Keywords:
Collective modes, affine invariance, integrable lattices, nonlinear elasticity

Affiliations:
Sławianowski J.J. - other affiliation
Kovalchuk V. - IPPT PAN
Sławianowska A. - other affiliation
Gołubowska B. - IPPT PAN
Martens A. - IPPT PAN
Rożko E.E. - IPPT PAN
Zawistowski Z.J. - IPPT PAN

List of recent monographs
1. 
Sławianowski J.J., Kovalchuk V., Sławianowska A., Gołubowska B., Martens A., Rożko E.E., Zawistowski Z.J., Invariant geodetic systems on Lie groups and affine models of internal and collective degrees of freedom, Prace IPPT - IFTR Reports, Warszawa, 7, pp.1-164, 2004

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