Related papers: Evaluating Sums over the Matsubara Frequencies
We cannot use directly the results of zero-temperature at finite temperature, for at finite temperature the average is to be carried over all highly degenerate excited states unlike zero-temperature average is only on unique ground state.…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
Nucleation rate computations are of broad importance in particle physics and cosmology. Perturbative calculations are often used to compute the nucleation rate $\Gamma$, but these are incomplete. We perform nonperturbative lattice…
We show that the Mellin summation technique (MST) is a well defined and useful tool to compute loop integrals at finite temperature in the imaginary-time formulation of thermal field theory, especially when interested in the infrared limit…
By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this…
Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature…
A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…
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…
The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…
We present a compressive sensing approach for the long standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary…
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 this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature…
Accurate calculations of the nucleation rate $\Gamma$ for first order phase transitions are important for determining their observable consequences in particle physics and cosmology. Perturbative calculations are often used, but they are…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…