English

Covariant gauge-natural conservation laws

Mathematical Physics 2009-11-10 v6 Differential Geometry math.MP

Abstract

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. {\em Vice versa} all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as {\em canonical} generators of covariant gauge-natural physical charges.

Keywords

Cite

@article{arxiv.math-ph/0406009,
  title  = {Covariant gauge-natural conservation laws},
  author = {Marcella Palese and Ekkehart Winterroth},
  journal= {arXiv preprint arXiv:math-ph/0406009},
  year   = {2009}
}

Comments

16 pages; presented at XXXVI Symposium on Math. Phys., Torun 09/06-12/06/04; the last paragraph of Section 3 has been reformulated, in particular a mistake in the equation governing the vertical part of gauge-natural lifts with respect to prolongations of principal connections (appearing e.g. in the vertical superpotential) has been corrected

R2 v1 2026-07-22T16:24:32.441Z