An Axiomatics and a Combinatorial Model of Creation/Annihilation Operators

TL;DR

This paper develops a categorical axiomatic framework and a combinatorial model for creation and annihilation operators on bosonic Fock space, exploring their commutation relations and coherent states.

Contribution

It introduces a novel categorical axiomatic theory and a combinatorial model for creation/annihilation operators, linking abstract theory with combinatorial structures.

Findings

Established a categorical axiomatic foundation for creation/annihilation operators

Presented a combinatorial model motivating the axiomatic theory

Analyzed commutation relations and coherent states within both frameworks

Abstract

A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.