This is an alternative version of the Rarita–Schwinger theory and a demonstration of some possibilities of generalizing the usual spin-3/2 description. The main result of this article follows from the redefinition of the Hermiticity condition and the space inversion symmetry. The version has been motivated by the understanding that a spin-3/2 particle is a phenomenon of nature by itself and therefore cannot be looked upon as composed by spin-1/2 and spin-1 particles. Hence, the spin-3/2 particle will not be subjected to the symmetry properties of spin-1/2 particle. If the standpoint mentioned above was admitted, then the Rarita–Schwinger spin-3/2 equation would be equivalent to the whole class of the Bhabha-type equations.

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A phenomenon present in many physical problems hodograph invariance of partial differential equations is considered for two-dimensional submanifolds in three-and four-dimensional spaces. This means that the equation keeps its shape when interchanging the roles of any of the functions and arguments, i. e. under a hodograph transformation. For that purpose unified formulations for hodograph transformations are obtained. A method for the formation of hodograph invariant equations is shown. The well-known scalar Born -Infeld equation and its two-component generalization prove to be based on hodograph quasi-invariant expressions.

The action integral of a relativistic string is generalized to n-dimensional objects in m-dimensional space. It can be brought to the action for m-n-component fields in ndimensional space. We call such object «sympleon». The corresponding equation is hodograph invariant via the equivalence of the initial coordinates. In the case of one-component field the scalar Born -Infeld equation is obtained.The action integral for a relativistic string, which is closely related to dual models [ l>2 ], is known to be