A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions Z[J ] to the lattice functional equations for field theories in the presence of an external source J . Using Grassmann polynomial expansions for the generating functional Z, we calculate propagators for systems of interacting fermions. These calculations are straightfo...

A general method is presented for calculating the field enhancement factor of cylindrically symmetric high aspect ratio conductive structures. A discrete distribution of charges is used on the symmetry axis to replace the real charge distribution such that the electrostatic potential satisfies a set of boundary conditions. Their number will be set through a self-validating process. The method i...

The background field method has been used successfully to determine hadron electromagnetic polarizabilities. Recently questions have been raised regarding the proper way to deal with the electric field on the lattice. In this paper, we show how the presence of a background electric field affects the quark hopping matrix. We use this formulation to carry out simulations on quenched configuration...

A cutoff regularization for a pure Yang-Mills theory is implemented within the background field method keeping explicit the gauge invariance of the effective action. The method has been applied to compute the beta function at one loop order.

These notes describe the multiconfigurational self-consistent-field (MCSCF) method, which is a general approach for describing chemical systems in which a single electron configuration is no longer an adequate description of the electronic structure. This commonly happens in reactions that break or form chemical bonds, diradicals, and metals of the first transition row. A single-determinant, re...

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form σ p p +m +V (r) are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential V (r) are investiga...

In this paper, we contribute a new B-spline based interval field decomposition method as non-probabilistic approach that takes into account local effects in modelling. With basis functions, the formulation is highly intuitive and easy to construct. The computational efficiency outperforms traditional method. explicit expression of proposed facilitates use optimisation methods determining bounds...