Nonlocal coherent states in an infinite array of boson sites

A regular coherent state (CS) is a special type of quantum state for boson particles placed in a single site. The defining feature of the CS is that it is an eigenmode of the annihilation operator. The construction easily generalizes to the case of a finite number of sites. However, the challenge is altogether different when one considers an infinite array of sites. In this work we demonstrate a mathematically rigorous construction that resolves the latter case. The resulting nonlocal coherent states (NCS) are simultaneous eigenmodes for all of the infinitely many annihilation operators acting in the infinite array's Fock space. Our construction fundamentally relies on Dirichlet series-based analysis and number theoretic arguments.