Zitterbewegung in Quantum Mechanics

Abstract

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.

Propagation of a relativistic electron wave packet in the Dirac equation

“…The position operator and its time evolution have been one of the main tools in investigating the Zitterbewegung [8,19,20]. A numerical approach recently has gained in popularity [13,[21][22][23][24][25].…”

The nature of the photon and the electron

“…Introducing the photon momentum observed in experiment, p = ω/c, gives a limit on the integral allowed angular momentum of the solutions of r h × p = . This sets the intrinsic scale of unit angular momentum for all solutions such as that described by equation (5). In conclusion, demanding the principle of absolute relativity, manifested in the form of equation (5), places strong restrictions on allowed solutions, over and above those required by the Maxwell equations alone.…”

“…In the usual parlance of the field one might talk of introducing the Lorentz group at this point (but perhaps not the Poincaré group -since general translations lie outside the allowed light-cone of the restrictions of absolute relativity). The closest match would then be to introduce the Clifford group corresponding to the space-time algebra Cl(1,3), 4,5 but that is not a division algebra, 1 which is widely thought to cause problems. 6 Imposing any of these a-priori, however reasonable they may appear, may introduce deep-held convictions of how a well-behaved mathematics should behave.…”

“…4 championed by Hestenes as the space-time algebra in internal models of the electron structure 5 and is a simplification, in some ways, of certain Dirac algebras. 13 The closest algebra discussed in the literature is sometimes called the Clifford-Dirac algebra and has been well-described in recent popular books 6 or more extensively in recent textbooks.…”

Zitterbewegung, internal momentum and spin of the circular travelling-wave electromagnetic model electron

“…Although a number of different interpretations of Ztg of Dirac model are given [9,[19][20][21][22][23][24][25][26][27], however, we will briefly review the interpretation given in [11,12].…”