Nonlinearn-pseudo fermions

Abstract

Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators a and b, b = a † , obeying the simple nonlinear anticommutation relation ab + b n a n = 1. The (n + 1)-order nilpotency of these operators follows from the existence of unique (up to a bi-normalization factor) avacuum. Supposing appropriate (n + 1)-order nilpotent para-Grassmann variables and integration rules the sets of n-pseudo-fermion number states, and '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.

Extended pseudo-fermions from non commutative bosons

“…For this reason, we call these particles, generalized pseudo-fermions. Other interesting generalizations of fermions could be found, for instance, in [17,18] and in [19].…”

Краткий Обзор Исследований Псевдобозонов, Псевдофермионов И Родственных Им Частиц

“…Заметим также, что аналогичные деформации ККС, КАС и др. рассматривались на протяжении многих лет несколькими другими авторами (см., например, [4], [5]).…”