Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles
arXiv:math-ph/0407054 · doi:10.1016/S0034-4877(05)80038-2
Abstract
By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in terms of the Hamiltonian connection canonically associated with a generalized Lagrangian obtained by contracting field equations.
12 pages, minor changes, references list updated; presented at XXXVI Symposium on Math. Phys., Torun 09/06-12/06/04; v4 to appear in Rep. Math. Phys
References in corpus (6)
- Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
- Covariant gauge-natural conservation laws
- The Hessian and Jacobi Morphisms for Higher Order Calculus of Variations
- Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
- Conservation Laws and Variational Sequences in Gauge-Natural Theories
- Second variational derivative of gauge-natural invariant Lagrangians and conservation laws
Cited by in corpus (6)
- Covariant gauge-natural conservation laws
- Lagrangian reductive structures on gauge-natural bundles
- Second variational derivative of gauge-natural invariant Lagrangians and conservation laws
- Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents
- Higgs fields induced by Yang--Mills type Lagrangians on gauge-natural prolongations of principal bundles
- Axiomatic classical (prequantum) field theory. Jet formalism