Canonical and Involutory Transformations of the Variational Problems of Transport Theory

The notions of canonical and involutory transformations from the calculus of variations are applied to neutron transport problems. It is shown that the variational formulations of Vladimirov, Selengut, Pomraning and Clark, and Davis are related through transformations of this type. It is pointed out that the pair of functionals indentified through the involutory transformation are reciprocal in the sense that the minimum of one is the maximum of the other. Implications of this fact for the development of approximation methods are discussed.