Generalization of Green's Theorem

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Abstract
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.

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