GAUGE CONSERVATION LAWS IN A GENERAL SETTING: SUPERPOTENTIAL

G. SARDANASHVILY
2009 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
The fact that the conserved current of a gauge symmetry is reduced to a superpotential is proved in a very general setting. In contrast with gauge symmetries, nontrivial Noether identities of Lagrangian field theory are well described in homology terms [5] [6] [7] [8] . Therefore, we define nontrivial gauge symmetries as those associated to complete nontrivial Noether identities in accordance with the second Noether theorem (Theorem 5). Given a nontrivial gauge symmetry of a Lagrangian L, the
more » ... Lagrangian L, the corresponding current J (12) is conserved by virtue of the first Noether theorem (Theorem 3). We prove that this current takes the superpotential form where the term W µ vanishes on the kernel of the Euler-Lagrange operator δL (3) of L and U νµ = −U µν is a superpotential (Theorem 6). 1047 1048 G. Sardanashvily
doi:10.1142/s0219887809003862 fatcat:cw7nuh6pb5dgdj3x3m2qmf4h5m