3rd CONFERENCE ON NONLINEARITY
4—8.09.2023, Belgrade, Serbia




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Branislav Sazdović

From Fock-Ivanenko covariant derivatives to non-Abelian and Poincare gauge theories

Abstract

Generally, derivatives measure difference between values of some field $\Psi^A (x)$ in neighboring points $x$ and $x + \Delta x$. Since we can compare fields only at the same point, to introduce derivatives we must use parallel transport of the field $\Psi^A (x)$ along some path. Then we can define derivatives which can be applied to the fields of arbitrary spin. We will call them Fock-Ivanenko covariant derivatives. With these derivatives we can use Leibniz product rule for the product of fields with different spins. Using this tool we can gauge any theory with given global symmetry algebra. We will present two examples: non-Abelian and Poincare gauge theories.