Nonlinear n-pseudo fermions

Abstract

Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators b and a, b ≠ a†, obeying the simple nonlinear anticommutation relation ab + bnan = 1. The (n + 1)-order nilpotency of these operators follows from the existence of unique (up to a bi-normalization factor) a-vacuum. Supposing appropriate (n + 1)-order nilpotent para-Grassmann variables and integration rules the sets of n-pseudo-fermion number states, ‘right’ and ‘left’ ladder operator bi-overcomplete sets of coherent states are constructed. Explicit examples of n-pseudo-fermion ladder operators are provided, and the relation of pseudo-fermions to finite level pseudo-Hermitian systems is briefly considered.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.