GENERALIZATION OF GREENS THEOREM

For a system of field equations which is derivable from a Lagrangian whose density is (i) homogeneous quadratic in the first derivatives of the field variables yA,μ and (ii) homogeneous of degree n in the undifferentiated field variables yA, one has the identity (n + 1)zALA(y) - yAMA(y, z) ≡ tρ, ρ, where MA(y, z) is the first-order change in the field equations LA(y) = 0 under the mapping yA → yA + zA. The specific example of general relativity is discussed.