Structure of the Poincaré Generators

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Abstract
The Poincaré generators for an open system augmented by the interaction parts of the full Poincaré generators are shown to satisfy a closed set of coupled differential equations having a form which is independent of the nature of the interaction parts. The differential equations are formulated in the hyperplane formalism, the differentiation being with respect to the hyperplane parameters. The general solutions of the equations are studied, yielding relations among the augmented generators that must be preserved in the limit of zero interaction, i.e., for a closed system. Introducing a hyperplane-dependent Hamiltonian density in a manner not implying local field theory, the obtained relations are shown to yield expressions for all the generators of a closed system in terms of the Hamiltonian density and its derivatives alone.

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