Symmetries in Lagrangian field theory

The paper presents a revision to the standard symmetry theory necessitated by a recent correction to the Cartan form. The Cartan form is used to determine the complete group of symmetries and corresponding conservation laws for a general Lagrangian L(x,Psi, Psi') with x = {x/sub i/}/sub i=1//sup n/, Psi = {Psi/sup α/}/sup κ//sub α=1/ = Psi' = {Psi/sub i//sup a/} = {∂Psi/sup α//∂x/sub i/}. This is the same as usual except now the term Ω/sup i/(L,ξ,eta) depends on the new Cartan form. Examples and explicit calculations for quadratic Lagrangians are given to point out the distinctions