Coherent states in fermionic Fock-Krein spaces and their amplitudes

TL;DR

This paper extends fermionic coherent states to Fock-Krein spaces with indefinite inner products, enabling their use in topological quantum field theory and deriving a universal amplitude formula for linear fields on manifolds with boundary.

Contribution

It introduces a generalization of fermionic coherent states to Fock-Krein spaces and derives a universal amplitude formula for linear field theories on manifolds with boundary.

Findings

Generalized fermionic coherent states to Fock-Krein spaces.

Derived a universal amplitude formula for coherent states.

Applicable to topological and boundary quantum field theories.

Abstract

We generalize the fermionic coherent states to the case of Fock-Krein spaces, i.e., Fock spaces with an idefinite inner product of Krein type. This allows for their application in topological or functorial quantum field theory and more specifically in general boundary quantum field theory. In this context we derive a universal formula for the amplitude of a coherent state in linear field theory on an arbitrary manifold with boundary.