Related papers: A beginner's guide to functional methods in partic…
Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory…
Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation…
We describe a new formulation of the functional renormalization group (RG) for interacting fermions within a Wilsonian momentum-shell approach. We show that the Luttinger-Ward functional is a fixed point of the RG, and derive the infinite…
The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
A new approach, "$\mathfrak{B}\text{-Function}$ Method", to the analysis of the reconstruction methods, phase space, and exact solutions of the alternative theories of gravity is suggested. The $\mathfrak{B}\text{-function}$ method which is…
We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this…
We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many…
The studies of Dyson-Schwinger Equations (DSEs) provide us with insights into nonperturbative phenomenon of quantum field theory. However, DSEs are essentially an infinite set of coupled Green's functions, it's necessary to decouple parts…
The route to reliable quantum nanoelectronic devices hinges on precise control of the electrostatic environment. For this reason, accurate methods for electrostatic simulations are essential in the design process. The most widespread…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
The LSND and MiniBoone seeming anomalies in neutrino oscillations are usually attributed to physics beyond the Standard model. It is, however, possible that they may be an artefact of the theoretical treatment of particle oscillations that…
Functional renormalization group (FRG) is an exact method for taking into account the effect of quantum fluctuations in the effective action of the system. The FRG method applied to effective theories of nuclear matter yields equation of…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…