Relativistic Transformation of Magnetic Dipole Moment

Abstract

Abstract-We consider three different definitions of magnetic dipole moment for electrically neutral compact bunches of charged particles and show that, in general, they are not equivalent to each other with respect to their relativistic transformation. In particular, we prove that the "configurational" definition of magnetic dipole moment m c = 1 2 V (r × j)dV (in the common designations) and its definition through generated electromagnetic field ("source" definition m s ) or experienced force ("force" definition m f ) lead to different relativistic transformations of m c and m s (m f ). The results obtained shed light on the available disagreements with respect to relativistic transformation of a magnetic dipole moment, and they can be used in covariant formulation of classical electrodynamics in material media.

Paving Through the Vacuum

“…This can be unified to if the original relation between the virtual fermion momentum and its size is rewritten as px = or the factor 2π is actually arriving from the difference of the fermion size and the average distance between fermion and antifermion. Note, that it is hard to choose the right expressions a priori due to the ambiguity for relativistic magnetic moment and dipole interactions as well as their Lorenz transformations [6,8].…”

“…where n k (p) is the virtual pair density for each family, defined in Equation (8). Ignoring the additional energy ε γ /2, the total length can be composed of x/4 = h/(4p) steps in the following way:…”