Conservation laws and variational sequences in gauge-natural theories (Q2725006)

The authors study the symmetries and conservation laws of higher-order Lagrangians on gauge-natural bundles by using the finite variational sequences by Krupka. Their main geometric tools are the concept of variational Lie derivative and a prolongation procedure transforming a principal connection on a principal bundle \(P\to M\) and a linear connection on \(M\) into a principal connection on the gauge-natural prolongation \(W^{(r,k)}P\) of the order \((r,k)\) of \(P\), \(r\leq k\). As an example, the authors show how their formalism enables one to obtain in a very straightforward way well known results concerning conserved quantities in the case of Einstein-Yang-Mills theories.