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The paper discusses the mathematical consequences of the application ofderived variables in gauge fields. Physics is aware of several phenomena, whichdepend first of all on velocities (like e.g., the force caused by chargesmoving in a magnetic field, or the Lorentz transformation). Applying theproperty of the second Noether theorem, that allowed generalised variables,this paper extends the article by Al-Kuwari and Taha (1991) with a newconclusion. They concluded that there are no extra conserved currentsassociated with local gauge invariance. We show, that in a more general case,there are further conserved Noether currents. In its method the paperreconstructs the clue introduced by Utiyama (1956, 1959) and followed byAl-Kuwari and Taha (1991) in the presence of a gauge field that depends on theco-ordinates of the velocity space. In this course we apply certain (but notfull) analogies with Mills (1989). We show, that handling the space-timecoordinates as implicit variables in the gauge field, reproduces the sameresults that have been derived in the configuration space (i.e., we do not loseinformation), while the proposed new treatment gives additional informationextending those. The result is an extra conserved Noether current.

Conserved Noether Currents, Utiyama's Theory of Invariant Variation, and Velocity Dependence in Local Gauge Invariance