arXiv subjects

Tomasz Radozycki

Publications and source records attributed to Tomasz Radozycki.

25 records · Page 2Linked to original sources

arXiv2008

Instantons and the infrared behavior of the fermion propagator in the Schwinger Model

Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.

hep-th↗

arXiv2007

Instanton modifications of the bound state singularity in the Schwinger Model

We consider the quark-antiquark Green's 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: $0,\pm 1, \pm 2$. 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 Green's 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.

hep-th↗

arXiv2006

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 Schrödinger 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.

quant-ph↗

arXiv2004

Quantum effects in the evolution of vortices in the electromagnetic field

We analyze the influence of electron-positron pairs creation on the motion of vortex lines in electromagnetic field. In our approach the electric and magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg effective Lagrangian. We show that these nonlinearities may change the evolution of vortices.

quant-ph↗

arXiv1998

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.

hep-th↗

arXiv1998

Four-point Green functions in the Schwinger Model

The evaluation of the 4-point Green functions in the 1+1 Schwinger model is presented both in momentum and coordinate space representations. The crucial role in our calculations play two Ward identities: i) the standard one, and ii) the chiral one. We demonstrate how the infinite set of Dyson-Schwinger equations is simplified, and is so reduced, that a given n-point Green function is expressed only through itself and lower ones. For the 4-point Green function, with two bosonic and two fermionic external `legs', a compact solution is given both in momentum and coordinate space representations. For the 4-fermion Green function a selfconsistent equation is written down in the momentum representation and a concrete solution is given in the coordinate space. This exact solution is further analyzed and we show that it contains a pole corresponding to the Schwinger boson. All detailed considerations given for various 4-point Green functions are easily generizable to higher functions.

hep-th↗

arXiv1997

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 shows the complete agreement between nonperturbative and perturbative approaches.

hep-th↗