1. Determinant/permanent division and direct mappings in Fock space
- Author
-
Quandt, Alexander
- Abstract
The standard mapping between different N-particle states in Fock space is very abstract and consists of combinations of creation and annihilation operators being formally applied to the vacuum state. The resulting formalism provides us with the correct symmetries in the case of fermions and bosons, but the permanents and Slater determinants that are formally joined by the action of these operators must be individually constructed from product states using symmetrizers and antisymmetrizers. Surely, this abstract approach does not correspond to a direct mapping between different N-particle states in Fock space. In the following, we will examine direct mappings in Fock space, which are generalizations of an old determinant division scheme by Schweins (1825). The suggested new scheme is based on a suitable definition of isolated states. We will show that all the classical results obtained by Schweins may be recovered. Furthermore, the new division scheme may easily be extended to permanents. This leads to direct mappings in Fock space, which correspond to creation and annihilation operators.
- Published
- 2023
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