Showing papers by "Vladimír Souček published in 1983"

Complex-quaternionic analysis applied to spin–½ massless fields

Abstract: In the paper the complex-quaternionic analysis and its spinor version is used for the study of integral formulas for spin ½ massless fields. The basic corrspondence between the complexified Fueter equation and the massless field equation (spin½) is described first, together with the corresponding Cauchy integral formulas. It is shown then how the complexified Cauchy integral formula can be used to give the connection between elliptic type (boundary value type) integral formulas on Euclidean spacetime and Kirchhoff type (initial value type) integral formulas on Minkowski space (for spin ½ massless fields). The explicit formulas showing such connection with the integral formula described by Penrose are given.

Operator formalism equivalent to the Feynman quantization technique

Abstract: The concept of a Fock–Stueckelberg space of quantum states and a procedure of an operator quantization using only Lagrangians (kinematical quantization) are introduced. A propagator operator K, matrix elements of which are Green’s functions, is used, and an equation of motion for it is derived. We prove that kinematical quantization is an operator (coordinate‐free) form of the Feynman quantization technique. The Feynman path integral (FPI) is obtained as a spectral representation of the operator K in a coordinate basis. The connection of a representation of commutation relations in this scheme, the domain of integration in FPI, and causality is mentioned.