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Classical and Quantized Affine Models of Structured Media

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Abstract

Having in view some applications in nanophysics, in particular in nanophysics of materials, we develop new dynamical models of structured bodies with affine internal degrees of freedom. In particular, we construct some models where not only kinematics but also dynamics of systems of affine bodies is affinely invariant. Quantization schemes are developed. This is necessary in the range of physical phenomena we are interested in.

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References

  1. Cosserat, E. and F., ‘Theorie des corps deformables’, in: Khvol’son, O.D., Traite de physique, translation by Davaux, E. 2nd edn, Hermann & Cie, Paris, Vol. 2, 1909, 953–1173.

  2. Eringen, A.C., ‘Mechanics of micromorphic continua’, in: Kröner, E. (ed), Proceedings of the IUTAM Symposium on Mechanics of Generalized Continua, Freudenstadt and Stuttgart, 1967, Springer, Berlin-Heidelberg-New York, Vol. 18, 1968, pp. 18–33.

  3. G. Capriz (1989) Continua with Microstructure NumberInSeriesVol. 35 Springer tracts in natural philosophy, Springer-Verlag New York- Berlin- Heidelberg- Paris -Tokyo

    Google Scholar 

  4. G. Capriz (2000) ArticleTitle‘Continua with substructure’ Phys. Mesomech. 3 IssueID5–14 37–50

    Google Scholar 

  5. G. Capriz P.M. Mariano (2003) ‘Balance at a junction among coherent interfaces in materials with substructure’ G. Capriz P.M. Mariano (Eds) Advances in Multifield Theories of Materials with Substructure Birkhäuser Basel

    Google Scholar 

  6. G. Capriz P.M. Mariano (2003) ArticleTitle‘Symmetries and Hamiltonian formalism for complex materials’ J. Elasticity 72 57–70 Occurrence Handle10.1023/B:ELAS.0000018775.44668.07 Occurrence Handle2005b:74007

    Article  MathSciNet  Google Scholar 

  7. P.M. Mariano (2001) ArticleTitle‘Multifield theories in mechanics of solids’ Adv. Appl. Mech. 38 1–93 Occurrence Handle2002j:74002

    MathSciNet  Google Scholar 

  8. G.W. Mackey (1963) The Mathematical Foundations of Quantum Mechanics Benjamin New York

    Google Scholar 

  9. J.J. Sławianowski V. Kovalchuk A. Sławianowska B. Gołubowska A. Mar-tens E.E. Rozko Z.J. Zawistowski (2004) ArticleTitle‘Affine symmetry in mechanics of collective and internal modes. Part I. Classical models’ Rep. Math. Phys. 54 IssueID3 373–427 Occurrence Handle2115746

    MathSciNet  Google Scholar 

  10. J.J. Sławianowski V. Kovalchuk A. Sławianowska B. Gołubowska A. Mar-tens E.E. Rozko Z.J. Zawistowski (2005) ArticleTitle‘Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models’ Rep. Math. Phys. 55 IssueID1 1–45 Occurrence Handle2126414

    MathSciNet  Google Scholar 

  11. V.I. Arnold (1978) Mathematical Methods of Classical Mechanics, Springer Graduate Texts in Mathematics NumberInSeriesVol. 60 Springer-Verlag New York

    Google Scholar 

  12. K. estpfahl (1967) Annalen der Physik 20 113

    Google Scholar 

  13. Ch. Kittel (1966) Introduction to Solid State Physics John Wiley & Sons Inc. New York

    Google Scholar 

  14. S.N. Levine (1965) Quantum Physics of Electronics The Maxmillan Company, New York, Collier-Maxmillan Limited London

    Google Scholar 

  15. R. Abraham J.E. Marsden (1978) Foundations of Mechanics EditionNumber2 The Benjamin-Cummings Publishing Company London-Amsterdam-Sydney-Tokyo

    Google Scholar 

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Correspondence to Jan J. Sławianowski.

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Sławianowski, J.J. Classical and Quantized Affine Models of Structured Media. Meccanica 40, 365–387 (2005). https://doi.org/10.1007/s11012-005-2105-2

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