| Title:
|
Gauge-natural field theories and Noether theorems: canonical covariant conserved currents (English) |
| Author:
|
Palese, Marcella |
| Author:
|
Winterroth, Ekkehart |
| Language:
|
English |
| Journal:
|
Proceedings of the 25th Winter School "Geometry and Physics" |
| Volume:
|
|
| Issue:
|
2005 |
| Year:
|
|
| Pages:
|
[161]-174 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms lying in the kernel of generalized Jacobi morphisms satisfy Bergmann-Bianchi identities and thus are generators of canonical covariant currents and superpotentials. As a consequence of the second Noether theorem, we further show that there exists a covariantly conserved current associated with the Lagrangian obtained by contracting the Euler-Lagrange morphism with a gauge-natural Jacobi vector field. We use as fundamental tools an invariant decomposition formul! (English) |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| MSC:
|
58E30 |
| MSC:
|
58E40 |
| MSC:
|
58J10 |
| MSC:
|
58J70 |
| MSC:
|
70S15 |
| MSC:
|
81T13 |
| idZBL:
|
Zbl 1113.58002 |
| idMR:
|
MR2287135 |
| . |
| Date available:
|
2009-07-13T21:55:23Z |
| Last updated:
|
2012-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701775 |
| . |
