Two-vortex structure of electron, nonlocality and Dirac equation

Abstract

The dimensionless electromagnetic coupling constant α = e 2 /hc may have three interpretations: as the well known ratio between the electron charge radius e 2 /mc 2 and the Compton wavelength of electron λc =h/mc, as a ratio of two angular momenta since Planck constant has the dimension of angular momentum, and two flux quanta e and hc/e. The anomalous part of the electron magnetic moment together with the unified picture of the three interpretations of α is suggested to have deep physical significance. The electric charge is proposed to be a new quantum of flux that leads to a new model of the electron envisaging a two-vortex structure. In analogy with quantum conditions we postulate sub-quantum conditions applicable in a region of the order of λc replacingh by a universal constant f = e 2 /2πc and apply it to Dirac equation in internal space that gives rise to the anomalous magnetic moment of electron. Dirac spinor and 2-spinor representation for vortex structure of electron in the single particle Dirac framework are discussed. The role of sub-quantum rules and the internal variables for developing the present ideas is also debated. A critical discussion on the past attempts to give fundamental importance to magnetism and flux quantum is given to delineate the new ideas in the present work.

Anomalous magnetic moment and vortex structure of the electron

“…The concentric ring for p = 1 may be identified with the second vortex having dimension equal to r e . This picture nicely fits the two-vortex Dirac electron model [12]. The multi-vortex structure can be envisaged for the geometry of the metric (45).…”

“…We are led to the hypothesis that electron spin has a fractional part f 2 , if expressed in units of Planck constant, and the electron charge has a mechanical origin as some kind of rotation. For further elucidation of this hypothesis see [9,10], and vortex model of the spatio-temporal bounded internal fields is developed in [11,12].…”

“…Even in QED, quite often, the intuitive picture of quantum vacuum effects is related to the size of the Compton wavelength. It is easily seen that in an alternative outlook [11,12] both length scales arise in the fine structure constant α = re λc , and magnetic moment becomes…”

Do phonons carry spin?

“…Fractional spin for quasi-particles is accepted in the literature, however to ascribe fractional spin f 2 to a free electron is a radical departure. Though the electron model proposed in [9,23] is based on this hypothesis the contribution of this paper is independent of any such model: we suggest the importance of anomalous magnetic moment and as-sociated spin in the magneto-mechanical effects in nano materials highlighted in [3,6]. In particular the angular momentum balance (1) and (2) must include electron fractional spin in the light of the sensitivity of measurements to detect phonon angular momentum as small as 10 −4 h.…”

Spintronics: Maxwell-Dirac theory, charge and spin

“…In the present paper we make this correspondence more definitive and study its novel implications on spintronics. Two-vortex internal structure of the electron [9] throws light on charge and spin transport in a unifying idea [10] that charge also has origin in the fractional spin.…”