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Autoparallels and the Inverse Problem of the Calculus of Variations.

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Τίτλος: Autoparallels and the Inverse Problem of the Calculus of Variations.
Συγγραφείς: Heisenberg, Lavinia1 (AUTHOR) heisenberg@thphys.uni-heidelberg.de
Πηγή: Fortschritte der Physik / Progress of Physics. May2026, Vol. 74 Issue 5, p1-9. 9p.
Θεματικοί όροι: *Calculus of variations, *Affine geometry, *General relativity (Physics), *Geometric connections, *Geodesics, *Variational approach (Mathematics)
Περίληψη: We prove that autoparallel curves associated with a torsion‐free but not necessarily metric‐compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational techniques that it produces the desired equations. Our analysis is based on systematically solving the inverse problem of the calculus of variation and the associated Helmholtz conditions. This demonstrates that the dynamics of autoparallels admit a consistent variational formulation even in the presence of non‐metricity. Our results provide a variational framework for particle motion in metric‐affine geometries and thereby contribute to the mathematical foundations of the geodesic principle in relativistic gravity. [ABSTRACT FROM AUTHOR]
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  Data: Autoparallels and the Inverse Problem of the Calculus of Variations.
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  Data: <searchLink fieldCode="AR" term="%22Heisenberg%2C+Lavinia%22">Heisenberg, Lavinia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> heisenberg@thphys.uni-heidelberg.de</i>
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  Data: <searchLink fieldCode="JN" term="%22Fortschritte+der+Physik+%2F+Progress+of+Physics%22">Fortschritte der Physik / Progress of Physics</searchLink>. May2026, Vol. 74 Issue 5, p1-9. 9p.
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  Data: *<searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br />*<searchLink fieldCode="DE" term="%22Affine+geometry%22">Affine geometry</searchLink><br />*<searchLink fieldCode="DE" term="%22General+relativity+%28Physics%29%22">General relativity (Physics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Geometric+connections%22">Geometric connections</searchLink><br />*<searchLink fieldCode="DE" term="%22Geodesics%22">Geodesics</searchLink><br />*<searchLink fieldCode="DE" term="%22Variational+approach+%28Mathematics%29%22">Variational approach (Mathematics)</searchLink>
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  Data: We prove that autoparallel curves associated with a torsion‐free but not necessarily metric‐compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational techniques that it produces the desired equations. Our analysis is based on systematically solving the inverse problem of the calculus of variation and the associated Helmholtz conditions. This demonstrates that the dynamics of autoparallels admit a consistent variational formulation even in the presence of non‐metricity. Our results provide a variational framework for particle motion in metric‐affine geometries and thereby contribute to the mathematical foundations of the geodesic principle in relativistic gravity. [ABSTRACT FROM AUTHOR]
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        Value: 10.1002/prop.70115
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        Text: English
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      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Affine geometry
        Type: general
      – SubjectFull: General relativity (Physics)
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      – SubjectFull: Geometric connections
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      – SubjectFull: Geodesics
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      – SubjectFull: Variational approach (Mathematics)
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      – TitleFull: Autoparallels and the Inverse Problem of the Calculus of Variations.
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              M: 05
              Text: May2026
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              Y: 2026
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