Extended phase space. I. Classical fields

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Abstract
Classical field theory is developed in the arena of extended phase space V8, the space of position, time, momentum, and energy. This enables one to incorporate Born’s reciprocity which demands equal status for the variables q and p. The present formulation is covariant under the extended Poincaré group P8 acting in V8. Variational methods for classical field theory are generalized. Besides the usual concept of the total 4-momentum, one encounters the notion of average position and time of the field distributions. The total charge emerges from a dynamical viewpoint. The Dirac and Duffin–Kemmer algebras are generalized in this setting. The corresponding wave equations would lead to a dynamical theory of the elementary particles. The symplectic structure is not considered because of the difficulties to represent spinors.

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