Related papers: A beginner's guide to functional methods in partic…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study the pion and kaon electromagnetic form factors and the $\gamma^\star \pi^0 \gamma$ transition form factor in impulse approximation. With model parameters…
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By…
Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in…
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable…
The quenched spectrum of glueballs with positive charge parity is calculated from two-body bound state equations. As input, a self-contained solution for the primitively divergent correlation functions from Dyson-Schwinger equations is…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation.…
In this series of lectures we present the universal method based on the use of the functional integrals to derive the bound state equations for different two-body systems in elementary particle physics as well as in condensed matter theory:…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
Dimensional reduction of finite temperature quantum field theories can be improved with help of continous renormalisation group steps. The method is applied to the integration of the lowest non-static ($n=\pm 1$) modes of the finite…
In this thesis we deal with different aspects of quantum field theory, particularly in non-perturbative but also perturbative regimes, applied to the intellectual construction that is the Standard Model for Particle Physics (SM), but also…
In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that the vertex functions defined by these equations can be used to truncate the exact…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions and compare the standard 2PI calculation with a modified version which uses a functional renormalization group method. The set of integral differential equations…
The 4PI effective action provides a a hierarchy of integral equations which have the form of Bethe-Salpeter equations. The vertex functions obtained from these equations can be used to truncate the exact renormalization group flow…
After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the $n$-point…
Using eigen-functional bosonization method, we study quantum many-particle systems, and show that the quantum many-particle problems end in to solve the differential equation of the phase fields which represent the particle correlation…
Although nonperturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…