Related papers: Perturbation Theory Without Diagrams: The Polaron …
The temperature phase transition in the N-component scalar field theory with spontaneous symmetry breaking is investigated in the perturbative approach. The second Legendre transform is used together with the consideration of the gap…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
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.…
Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At…
A new method for analyzing second-order phase transitions is presented and applied to the polaronic system La$_{0.7}$Ca$_{0.3}$MnO$_{3}$. It utilizes heat capacity and thermal expansion data simultaneously to correctly predict the critical…
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.…
From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a…
A perturbation expansion is considered about the Ohta-Jasnow-Kawasaki theory of phase-ordering dynamics; the non-linear terms neglected in the OJK calculation are reinstated and treated as a perturbation to the linearised equation. The…
In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
We exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation. Among other things we use the formalism to develop a good analytic…
In order to describe properties of an equilibrated quark-gluon plasma, QCD at finite temperature (and density) has to be considered. Besides lattice calculations, which can be applied only to static quantities at zero density, perturbative…
A new computational idea for continuum quantum field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating…
We calculate the nucleons' electromagnetic polarizabilities in heavy baryon chiral perturbation theory including all terms to order ${\cal O} (q^4)$. The chiral prediction of the electric polarizabilities for the neutron and the proton are…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
In this paper we study the hard-thermal-loop effective theory at next-to-leading order. Standard power-counting predicts that a large number of diagrams, including 2-loop diagrams, may need to be calculated. In all of the calculations that…
In the first order of the perturbation theory, the correction to the electronic terms of a diatomic molecule is calculated taking into account the Pauli principle.
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body…