Geometric nonlinearities in field theory, condensed matter and analytical mechanics
There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essen...
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| Format: | Article |
| Language: | English |
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Institute for Condensed Matter Physics
2010-01-01
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| Series: | Condensed Matter Physics |
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| Online Access: | http://dx.doi.org/10.5488/CMP.13.43103 |
| _version_ | 1819043356928376832 |
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| author | J.J. Sławianowski |
| author_facet | J.J. Sławianowski |
| author_sort | J.J. Sławianowski |
| collection | DOAJ |
| description | There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essential, non-perturbative nonlinearities which are not described by correction terms imposed on some well-defined linear background. Our idea in this paper is that there exists some mysterious, still incomprehensible link between essential, physically relevant nonlinearity and dynamical symmetry, first of all, of large symmetry groups. In some sense the problem is known even in soliton theory, where the essential nonlinearity is often accompanied by the infinite system of integrals of motion, thus, by infinite-dimensional symmetry groups. Here we discuss some more familiar problems from the realm of field theory, condensed matter physics, and analytical mechanics, where the link between essential nonlinearity and high symmetry is obvious, although not fully understandable. |
| first_indexed | 2024-12-21T09:55:29Z |
| format | Article |
| id | doaj.art-3e121b663dca494b840a7fa5f236a03d |
| institution | Directory Open Access Journal |
| issn | 1607-324X |
| language | English |
| last_indexed | 2024-12-21T09:55:29Z |
| publishDate | 2010-01-01 |
| publisher | Institute for Condensed Matter Physics |
| record_format | Article |
| series | Condensed Matter Physics |
| spelling | doaj.art-3e121b663dca494b840a7fa5f236a03d2022-12-21T19:08:05ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2010-01-0113443103Geometric nonlinearities in field theory, condensed matter and analytical mechanicsJ.J. SławianowskiThere are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essential, non-perturbative nonlinearities which are not described by correction terms imposed on some well-defined linear background. Our idea in this paper is that there exists some mysterious, still incomprehensible link between essential, physically relevant nonlinearity and dynamical symmetry, first of all, of large symmetry groups. In some sense the problem is known even in soliton theory, where the essential nonlinearity is often accompanied by the infinite system of integrals of motion, thus, by infinite-dimensional symmetry groups. Here we discuss some more familiar problems from the realm of field theory, condensed matter physics, and analytical mechanics, where the link between essential nonlinearity and high symmetry is obvious, although not fully understandable.http://dx.doi.org/10.5488/CMP.13.43103Born-Infeld electrodynamicscondensed mattergeneral relativity and tetradsnon-perturbative nonlinearityrelativistic structured continuumdynamical symmetry |
| spellingShingle | J.J. Sławianowski Geometric nonlinearities in field theory, condensed matter and analytical mechanics Condensed Matter Physics Born-Infeld electrodynamics condensed matter general relativity and tetrads non-perturbative nonlinearity relativistic structured continuum dynamical symmetry |
| title | Geometric nonlinearities in field theory, condensed matter and analytical mechanics |
| title_full | Geometric nonlinearities in field theory, condensed matter and analytical mechanics |
| title_fullStr | Geometric nonlinearities in field theory, condensed matter and analytical mechanics |
| title_full_unstemmed | Geometric nonlinearities in field theory, condensed matter and analytical mechanics |
| title_short | Geometric nonlinearities in field theory, condensed matter and analytical mechanics |
| title_sort | geometric nonlinearities in field theory condensed matter and analytical mechanics |
| topic | Born-Infeld electrodynamics condensed matter general relativity and tetrads non-perturbative nonlinearity relativistic structured continuum dynamical symmetry |
| url | http://dx.doi.org/10.5488/CMP.13.43103 |
| work_keys_str_mv | AT jjsławianowski geometricnonlinearitiesinfieldtheorycondensedmatterandanalyticalmechanics |