Combinatorial Models of Creation-Annihilation

Understand

Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1.

• This study surveys the relationships between classical combinatorial structures and the reduction to normal form of operator polynomials in such an algebra.
• The connection is achieved through suitable labelled graphs, or "diagrams", that are composed of elementary "gates".
• In this way, many normal form evaluations can be systematically obtained, thanks to models that involve set partitions, permutations, increasing trees, as well as weighted lattice paths.