Space-Time Algebra of Sedeons Electrodynamics, Hydrodynamics, Field Theory, and Quantum Mechanics

This book is a comprehensive guide to the space-time algebra of sixteen-component values "sedeons". This algebra is designed to provide a compact representation of equations that describe various physical systems. The book considers the symmetry of physical quantities concerning the operations of spatial and temporal inversion. This approach allows the formulation of a wide class of mathematical physics equations within a unified framework and enables the generalization of these equations for essential problems in electrodynamics, hydrodynamics, plasma physics, field theory, and quantum mechanics. In particular, it is shown that the broken symmetry between electricity and magnetism in electrodynamics equations is a result of choosing an asymmetric representation of these phenomena. The sedeonic algebra enables the formulation of Maxwell-like equations for the fields with a nonzero mass of quantum, which facilitates the calculation of energy for baryon-baryon interaction and the semi-classical interpretation of this interaction. It also allows one to generalize the hydrodynamics equations for the case of vortex turbulent flows and for a hydrodynamic two-fluid model of electron-ion plasma.