arXiv subjects

Vladimir Sauli

Publications and source records attributed to Vladimir Sauli.

26 records · Page 2Linked to original sources

arXiv2009

Confinement of electrons in QED2+1 and quarks in QCD3+1 in Temporal Euclidean space

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. QCD quark gap equation is solved in the framework of Temporal Euclidean space as well. In both models, the obtained complex fermion propagators exhibits confinement, since it does not satisfies Khallen-Lehmann representation.

hep-ph↗

arXiv2006

Solution of Dynamical Spontaneous Chiral Symmetry Breaking in Minkowski Space, Linearized approximation

Chiral symmetry breaking and mass generation is studied in a vectorial, confining asymptotic free gauge theory. Using the Schwinger-Dyson equation in improved ladder approximation, we calculate the fermion propagator in the whole Minkowski space. The estimate for $f_π$ and the dependence of physical mass on a coupling strength is provided. We focus on the extraction of spectral function of fermion propagator in the strongly coupled regime. Our calculations indicate that up to the crossover between walking and QCD-like running dynamics, the real pole of the propagator is not excluded and very likely it is actually developed at zero temperature theory.

hep-ph↗

arXiv2006

Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space

We review some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral representation in QFT and a discussion of renormalization in this approach. The technique based on the integral representation of Green's functions is exploited to solve Schwinger-Dyson equations in several quantum field models, eg. in scalar models and in strong coupling $QED_{3+1}$ in the quenched and in the unquenched approximation. The phenomenon of dynamical chiral symmetry breaking in regularized theory is touched. In QCD, the analyticity of gluon propagator on the complex momentum square plane is exploited to continue some recent lattice data to timelike momentum axis. We find non-positive absorptive part contribution in the Landau gauge gluon propagator which is in agreement with some other new recent analyzes.

hep-ph↗

arXiv2005

Some Analytical Aspects in Field Theories with Dynamical Mass Generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looking for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand by hand with the nontrivial solution for mass function. The consequences are discussed.

hep-ph↗

arXiv2004

Minkowski solution of Dyson-Schwinger equations in momentum subtraction scheme

Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with massive pseudoscalar meson and conventional spinor QED. Within the momentum subtraction procedure, the appropriate renormalization is performed analytically which leads to the usual dispersion formulation. The electron propagator obtained in this frame is compared with the solution of Euclidean Dyson-Schwinger equation and with the perturbation theory results as well. The proposed method has the advantage of obtaining solutions in both the space- and {\bf{time}}-like regimes of momenta. In addition,when the coupling constant increases we find some un-expected discrepancy between the Euclidean and integral representation solutions. Especially, when the solutions of the original momentum DSE's exhibit the signal for confinement then the spectral approach gives no solution for Lehmann function of confined particle.

hep-ph↗

arXiv2004

Running coupling and fermion mass in strong coupling QED

Simple toy model is used in order to exhibit the technique of extracting the non-perturbative information about Green's functions in Minkowski space. The effective charge and the dynamical electron mass are calculated in strong coupling 3+1 QED by solving the coupled Dyson-Schwinger equations for electron and photon propagators. The minimal Ball-Chiu vertex was used for simplicity and we impose the Landau gauge fixing on QED action. The solution obtained separately in Euclidean and Minkowski space were compared, the latter one was extracted with the help of spectral technique.

hep-ph↗

arXiv2002

Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism

The Bethe-Salpeter equation for Wick-Cutkosky like models is solved in dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger equations for propagators is combined with the dressed ladder Bethe-Salpeter equation for the scalar S-wave bound state amplitudes. With the help of spectral representation the results are obtained directly in Minkowski space. We give a new analytic formula for the resulting equation simplifying the numerical treatment. The bare ladder approximation of Bethe-Salpeter equation is compared with the one with dressed ladder. The elastic electromagnetic form factors is calculated within the relativistic impulse approximation.

hep-ph↗

arXiv2001

Formfactor of the relativistic scalar bound state calculated in Minkowski space

We have calculated the electromagnetic elastic form factor of a two body scalar bound state. The Bethe-Salpeter equation is solved directly in the Minkowski space using the Perturbation Theory Integral Representation. At soft coupling regime the obtained results are compared with those following from a quasipotential spectator (Gross) approximation.

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