Fermion propagator is computed in a simple model on an extremely anisotropic lattice ξ ≫ 1. Fermion determinant is evaluated up to ξ−4 order. Chiral condensate is estimated in mean field approximation.

In this paper, we present solutions to the fermion mass hierarchy problem in the context of the minimal supersymmetric standard theory augmented by an anomalous family–dependent U(1)X symmetry. The latter is spontaneously broken by non–zero vevs of a pair of singlet fields whose magnitude is determined through the D– and F–flatness conditions of the superpotential. We derive the general solutio...

We prove unbroken symmetry of grading transformations multiplying all fermion field operators by −1. We give a criterion of spontaneously symmetry breaking for general quasi-local systems with any statistics called macroscopic spontaneously symmetry breaking, or for short MSSB. It is formulated based on our thermodynamical viewpoint that each pair of distinct phases (appeared in spontaneous sym...

We study the QCD scattering amplitudes for q̄q → gg and q̄q → ggg where q is a massive fermion. Using a particular choice of massive fermion spinor we are able to derive very compact expressions for the partial spin amplitudes for the 2 → 2 process. We then investigate the corresponding 2 → 3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we again de...

We introduce a criterion named macroscopic spontaneously symmetry breaking, for short MSSB, for general quasi-local systems with any statistics. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every outside system of a local region specified by the given quasi-local str...