Related papers: Feynman parametrization and Mellin summation at fi…

The classical Heisenberg type spin Hamiltonian is widely used for simulations of finite temperature properties of magnetic metals often using parameters derived from first principles calculations. In itinerant electron systems, however, the…

We prove in full generality the thermal operator representation for Matsubara sums in a relativistic field theory of scalar and fermionic particles. It states that the full result of performing the Matsubara sum associated to any given…

We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the…

At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are…

We impose the periodicity conditions corresponding to the Matsubara formalism for Thermal Field Theory as constraints in the imaginary time path integral. These constraints are introduced by means of time-independent auxiliary fields which,…

In order to compress and more easily interpret Lyman-$\alpha$ forest (Ly$\alpha$F) datasets, summary statistics, e.g. the power spectrum, are commonly used. However, such summaries unavoidably lose some information, weakening the…

Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…

In these lectures we introduce the Feynman-Schwinger representation method for solving nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving…

As powerful as machine learning (ML) techniques are in solving problems involving data with large dimensionality, explaining the results from the fitted parameters remains a challenging task of utmost importance, especially in physics…

I describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given…

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…

We construct a program to calculate Feynman amplitudes at finite temperature in the real time Keldysh formalism using the symbolic manipulation program {\it Mathematica}. As an example, the usefulness of this program is demonstrated by…

A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD)…

Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…

A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in…

Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree…

Mermin's dielectric function [N.D. Mermin, Phys. Rev. B 1, 2362 (1970)] is widely assumed to satisfy the f-sum rule because he constrains his ansatz with the continuity equation. However, we identify a moment-closure problem in Mermin's use…

Calculation of hadronization, decay or scattering processes at non-zero temperatures and densities within the Nambu-Jona-Lasinio-like models requires some techniques for computation of Feynmann diagrams. Decomposition of Feynman diagrams at…

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

We present an algorithm to evaluate Matsubara sums for Feynman diagrams comprised of bare Green's functions with single-band dispersions with local U Hubbard interaction vertices. The algorithm provides an exact construction of the analytic…