University of La Laguna, Spain
Title: Classical Lagrangian formulation of local gauge U(1) and SU(3) fields in terms of field strength magnitudes described in Weyl two-spinor language and induced Zitterbewegung (trembling motion) in spin 1/2 particles via gauge field U(1) transformations
Biography: J Buitrago
After a discussion about classical local U(1) and SU(3) gauge invariance theories in Weyl two-spinor form (in terms of the electric and magnetic field strength components as well as the color field components) and the associated two spinor equations equivalent to the Lorentz Force equation of electrodynamics. The local U(1) gauge transformation properties of the different components of the symmetric second order electromagnetic field spinor are analyzed. It is found that only the third component of the magnetic field is changed by local gauge transformations. Using the gauge freedom associated with the third component of the magnetic field and choosing a specific gauge (in a somewhat similar manner as the familiar Coulomb gauge in QED) it is shown that the phenomenon of Zitterbewegung (trembling motion) appears in a natural way as internal motion with the velocity of light applicable to any one-half spin particle thus suggesting a kinematic origin of its rest mass and helicity. This result is in sharp contrast with the traditional interpretation (emerging from the Dirac equation) as transitions between positive and negative energy states.