Workshop
The Fermi-Dirac algebra and Hamiltonians
- Svala Sverrisdóttir
Abstract
In quantum chemistry, many-electron states are represented as elements of an exterior algebra, the Fock space. The fermionic creation and annihilation operators generate the Fermi-Dirac algebra, which can be realized as a Clifford algebra acting on the Fock space. The elements of the Fermi–Dirac algebra act as endomorphisms of the Fock space. Among these are the two-body electronic Hamiltonian and the cluster operator. Their structure leads to identities that truncate the Baker-Campbell-Hausdorff expansion, thereby allowing us to express the coupled cluster equations as a polynomial system of degree at most four.
