The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles

Abstract

Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single nonhomogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and their symmetries highlighted: massless photons with magnetic monopoles and finite photon mass in the absence of monopoles. Finally, it is shown that the EM-duality invariance is a symmetry of the Hamiltonian density (for Minkowskian spacetime) and Lagrangian density (for Euclidean 4-space) that reflects the signature of the respective metric manifold.

Thermodynamic aspects of information transfer in complex dynamical systems

“…In classical electrodynamics, for instance, the electric charge is the conserved quantity, ρ is the electric charge density, and j is the electric current density [27]. A similar line of reasoning appears in fluid dynamics, thermodynamics, and quantum theory where the electric charge is replaced with mass, heat, and probability distributions, respectively.…”

Associative Space-Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory

“…The operations of time inversion ( ) R t , space inversion ( ) R r and space-time inversion ( ) R tr are connected with transformations in e 1 , e 2 , e 3 basis and can be presented as (27) …”

“…It remains constant under the transformations of space and time inversion (27). Time quaternion q t  , space quaternion q r  and space-time quaternion q tr  are transformed under inversions in accordance with the commutation rules for the basis elements e t , e r , e tr .…”

“…Time quaternion q t  , space quaternion q r  and space-time quaternion q tr  are transformed under inversions in accordance with the commutation rules for the basis elements e t , e r , e tr . For example, performing the operation of time inversion (see (27)) with the quaternion q t  we obtain the conjugated quaternion …”

“…It can be considered as the equation for the force massive field [27]. In this case the parameter m 0 is the mass of quantum of field and  W is field potential.…”