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Canonical and Lagrangian formalism in full correct, dual symmetrical form, for the classical bispinor and vector-pseudovector fields in interaction

The full correct Lagrangian as well as canonical formalism for a classical bispinor and vector- pseudovector fields in interaction has here been developed in dual symmetrical form. Interaction between bispinor and vector-pseudovector field is introduced almost by the minimal way. The vector- pseudovector fields are almost gauge fields. Lagrange equations for all fields are second order equations, and for the vector and pseudovector fields equations are coupled. Canonical equations for all fields are of the first order and for the bispinor field should be transformed to two coupled Dirac like equations with opposite mass terms. Canonical equations for the vector and pseudovector field are Maxwell's like equations, but because of symmetry of the Lagrange's density, two types of currents, vector and pseudovector (electric charge and magnetic pseudocharge) current appear naturally. The symmetry properties of Lagrangian have been considered. Constants of motion are analyzed.

Canonical, Lagrangian, formalism, dual, symmetry, classical, bispinor, vector, pseudovector, field, interaction

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