Yungang Lu
We introduce the (q,2)-Fock space over a given Hilbert space, calculate the explicit form of a product of the creation and annihilation operators acting on the vacuum vector, demonstrate that this explicit form involves a specific subset of the set of all pair partitions, and provide a detailed characterization of this subset.
This paper contains 6 sections, 9 theorems, 110 equations.
Proposition 2.5
Let $\mathcal{H}$ be a Hilbert space and let $q$ belong to $[-1,1]$. For any $f\in\mathcal{H}$, the $(q,2)-$creation operator $A^+(f)$ is bounded and So, $A(f):=(A^+(f))^*$ is well--defined, named as the $(q,2)-$annihilation operator with the test function $f\in \mathcal{H}$. Moreover, for any $f\in \mathcal{H}$, hold the following statements: 1) $A(f)\Phi=0$ and for any $n\in\mathbb{N}^*$, $\{g_
