# Project CRDSE – Dyson-Schwinger Variationszugang zur Quantenfeldtheorie

## Basic data

Acronym:

CRDSE

Title:

Dyson-Schwinger Variationszugang zur Quantenfeldtheorie

Duration:

01/07/2015 to 30/06/2018

Abstract / short description:

The goal of the intended research project is the development of a general non-perturbative Hamiltonian approach to quantum field theory in the continuum, which is based on a variational principle with non-Gaussian vacuum wave functionals. To this end, the wave functional is written as the exponent of an "action", which is expanded in powers of the fields. The non-local kernels (variational kernels) appearing as expansion coefficients will be determined by minimising the vacuum energy density. The center piece of the approach are generalized Dyson-Schwinger equations (DSEs) which allow to express the n-point functions of the fields (and, in particular, the energy) by the variational kernels. This approach leads to a system of equations of motion which contains, besides the generalized DSEs, also the gap equations for the variational kernels obtained by minimizing the energy. This system of integral equations has to be solved self-consistently. The aproach is not restricted to relativistic quantum field theories, but is also well suited for a non-perturbatibve treatment of interacting many-body systems and allows a systematic improvement of the mean field approximation. Specifically, the approach shall be worked out for QCD in Coulomb gauge. For this purpose, a vcuum wave functional is used which contains in the exponent up to quartic terms in the gauge field, as well as the coupling of the quarks to the gluons. In a first step, the resulting equations of motion shall be solved analytically by power expansion in momentum space for the n-point functions in both the IR and the UV. Subsequently, these equations shall be solved numerically in the entire momentum region. This shall be done first in the so-called quenched approxmation, and subsequently also in an unquenched calculation.

Keywords:

Hamilton-Formuleriung zur Quantenfeldtheorie

Nicht-Gaußsche Wellenfunktionale

Coulomb-Eichung

Variationszugang

## Involved staff

### Managers

Faculty of Science

University of Tübingen

University of Tübingen

Institute for Theoretical Physics (ITP)

Department of Physics, Faculty of Science

Department of Physics, Faculty of Science

## Local organizational units

Institute for Theoretical Physics (ITP)

Department of Physics

Faculty of Science

Faculty of Science

## Funders

Bonn, Nordrhein-Westfalen, Germany