Free Fock space and functional calculus approach to the n-point information about the "Universe"

TL;DR

This paper develops a mathematical framework using free Fock space and functional calculus to analyze the n-point information of the universe, deriving equations from a fundamental differential equation for a unique field.

Contribution

It introduces a novel approach combining free Fock space and functional calculus to derive and analyze equations for n-point information in a physical field.

Findings

Derived equations for n-point information using free Fock space.

Extended operators reveal the physical vacuum vector with global field characteristics.

Analyzed resolvent regularization for the original systems with functional calculus.

Abstract

Starting from a differential equation for the unique field, the equation for the generating vector |V> of the n-point information (correlation and smeared functions) in the free Fock space is derived. In derived equation, due to appropriate extension of the right invertible operators, the physical vacuum vector |0> appears with a global characteristic of the field. For so called resolvent regularization of the original systems, the closed equations for the n-point information are analysed with the help of functional calculus.