Coherent states in the fermionic Fock space

TL;DR

This paper constructs fermionic coherent states within the Fock space framework, adapting methods for infinite dimensions, and demonstrates that this space forms a reproducing kernel Hilbert space of holomorphic functions.

Contribution

It introduces a novel construction of fermionic coherent states suitable for infinite-dimensional Fock spaces, extending existing finite-dimensional approaches.

Findings

Fermionic coherent states are explicitly constructed.

Fock space is shown to be a reproducing kernel Hilbert space.

The approach is adapted for infinite-dimensional cases.

Abstract

We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.