Nonlinear n-Pseudo Fermions

Abstract

Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators $a$ and $b$, $b\ne a^{†}$, 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) $a$-vacuum. 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.

10 pages, no figures; minor corrections, accepted in J. Phys. A

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Cited by in corpus (1)

• Extended pseudo-fermions from non commutative bosons