Relational Analysis of Dirac Equation in Momentum Representation
arXiv:2208.07435 · doi:10.1134/S0202289322040119
Abstract
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations (BSCR) between elements of two abstract sets. With the derivation performed we show that the 4-dimensional pseudo-Euclidean momentum space is not needed a priori but naturally emerges from considerations of rather general character (2-spinor algebra). A bispinor wave function is constructed for a fermion with positive energy and an arbitrary distribution of momenta. Special attention is paid to physical assumptions that should be made to enable the construction.
LaTeX, 16 pages, 3 new references were added, submitted to Gravitation and Cosmology, minor corrections