1203.3937 (D. A. Trifonov)

Nonlinear $n$-Pseudo Fermions    [PDF]

D. A. Trifonov

Nonlinear pseudo-Hermitian 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.

View original: http://arxiv.org/abs/1203.3937