Nonlinear n-Pseudo Fermions

Details Nonlinear n-Pseudo Fermions Nonlinear n-Pseudo Fermions

2012-03-18

arxiv.org/abs/1203.3937v2

Physics

Quantum Physics

10 pages, no figures; minor corrections

Scientific paper

Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators b and a, b \neq a^\dagger, 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) $a$-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 biefly considered.

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