Riemann-Lagrange geometrical background for multi-time physical fields (Q2770054)
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scientific article; zbMATH DE number 1702491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Riemann-Lagrange geometrical background for multi-time physical fields |
scientific article; zbMATH DE number 1702491 |
Statements
20 February 2002
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jet bundles
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Lagrangians
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connections
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0.91557527
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0.90017617
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0.86718446
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Riemann-Lagrange geometrical background for multi-time physical fields (English)
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A general geometrical framework for multi-time field theories is proposed. As geometrical space the 1-jet bundle \(J^1(T,M) \rightarrow T \times M\) of smooth manifolds \(T\) and \(M\) is used. The Lagrangian is \(L= h_{\alpha \beta} g^{ij}x^i_{\alpha}x^j_{\beta} +U^{(i)}_{(\alpha)}x^i_{\alpha} + F(t,x)\). A nonlinear connection is derived and a canonical connection of Cartan type is considered. Torsions and curvatures of these connection are computed. Various links to field theory are pointed out.
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