Equivalence Theorem for Higher Order Equations

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We show that the theory of an nth-order field equation, minimally coupled to electromagnetism, is completely equivalent to the theory of n independent second-order equations, also minimally coupled to the electromagnetic field. The equivalence is shown to hold as an algebraic identity between the respective matrix elements for a given order of the perturbative solution. A general functional proof is also given. The equivalence shows that the higher order theory is both renormalizable and unitary.

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