@MISC{Khrapko01thechange, author = {R. I. Khrapko and Ai Ai ∂if}, title = {The change}, year = {2001} }

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Abstract

F. V. Gubarev et al. [4] have argued that the minimum value of the volume integral of the vector potential squared may have physical meaning, in defiance of the equivalence of potentials which are connected by the gauge transformations. Earlier, R. I. Khrapko proposed a gauge noninvariant electrodynamics spin tensor [1]. The standard electrodynamics spin tensor is zero. Here we point out that the Biot-Savarat formula uniquely results in a preferred, “true ” vector potential field which is generated from a given magnetic field. A similar integral formula uniquely permits to find a “true ” scalar potential field generated from a given electric field even in the case of a nonpotential electric field. A conception of differential forms is used. We say that an exterior derivative of a form is the boundary of this form and the integration of a form by the Biot-Savarat-type formula results in a new form named the generation. Generating from a generation yields zero. The boundary of a boundary is zero. A boundary is closed. A generation is sterile. A conjugation is considered. The conjugation converts closed forms to sterile forms and back. It permits to construct chains of forms. The conjunction differs from the Hodge star operation: the conjugation does not imply the dualization. A circularly polarized wave is considered in view of the electrodynamics spin tensor problem. 1. The gauge equivalence of differential forms It is obvious that in a static case we can add a constant φ0 to an electric scalar potential φ and we can add a gradient ∂if to a magnetic vector potential Ai without changing the corresponding electric Ei and magnetic Bij fields. Indeed,