Tomasz Radozycki

Pinning and transport of cyclotron (Landau) orbits by electromagnetic vortices

Electromagnetic waves with phase defects in the form of vortex lines combined with a constant magnetic field are shown to pin down cyclotron orbits Landau orbits in the quantum mechanical setting of charged particles at the location of the vortex. This effect manifests itself in classical theory as a trapping of trajectories and in quantum theory as a Gaussian shape of the localized wave functions. Analytic solutions of the Lorentz equation in the classical case and of the Schrodinger or Dirac equations in the quantum case are exhibited that give precise criteria for the localization of the orbits. There is a range of parameters where the localization is destroyed by the parametric resonance. Pinning of orbits allows for their controlled positioning: They can be transported by the motion of the vortex lines.

Summing up the perturbation series in the Schwinger Model

Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation, performed entirely in momentum space, shows the complete agreement between nonperturbative and perturbative approaches.

Schwinger model Green functions with topological effects

The fermion propagator and the 4-fermion Green function in the massless QED2 are explicitly found with topological effects taken into account. The corrections due to instanton sectors k=+1,-1, contributing to the propagator, are shown to be just the homogenous terms admitted by the Dyson-Schwinger equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are included into consideration. The quark condensates are then calculated and are shown to satisfy cluster property. The theta-dependence exhibited by the Green functions corresponds to and may be removed by performing certain chiral gauge transformation.

Instanton modifications of the bound state singularity in the Schwinger model

We consider the quark-antiquark Greens function in the Schwinger model with instanton contributions taken into account. Thanks to the fact that this function may analytically be found, we draw out singular terms, which arise due to the formation of the bound state in the theory--the massive Schwinger boson. The principal term has a pole character. The residue in this pole contains contributions from various instanton sectors: 0, {+-}1, {+-}2. It is shown that the nonzero ones change the factorizability property. The formula for the residue is compared to the Bethe-Salpeter wave function found as a field amplitude. Next, it is demonstrated, that apart from polar part, there appears in the Greens function also the weak branch point singularity of the logarithmic and dilogarithmic nature. These results are not in variance with the universally adopted S-matrix factorization.

Relative variables of the exact fermion-antifermion bound state wave function in the Schwinger model

The Bethe-Salpeter amplitude for the fermion-antifermion bound state in the Schwinger model is investigated. The dependence on the relative time and position in the center-of-mass frame in all contributing instanton sectors is analyzed. The same is accomplished for the relative energy and momentum variables. Several interesting properties of the amplitude are revealed. The explicit threshold structure is demonstrated.

Relative-energy dependence of the Bethe–Salpeter amplitude in two-dimensional massless QED

The exact

Quantum effects in the evolution of vortices in the electromagnetic field.

q\bar{q}

Infrared self-consistent solutions of bispinor

qq¯ Bethe–Salpeter bound state amplitude is investigated in the space of relative energy