The Dirac Sea for the Non-Separable Hilbert Spaces

TL;DR

This paper rigorously constructs the Dirac Sea for fermionic quantization within non-separable Hilbert spaces, showing that these representations depend on the Axiom of Choice but are unitarily equivalent to the classic Fock representation.

Contribution

It introduces a rigorous construction of the Dirac Sea in non-separable Hilbert spaces, expanding the mathematical framework of fermionic quantization.

Findings

Dependence on the Axiom of Choice for CAR-representations

Unitary equivalence to the classic Fock representation

Extension of Dirac Sea construction to non-separable spaces

Abstract

We give a rigorous construction of the Dirac Sea for the fermionic quantization in the non-separable Hilbert spaces. These CAR-representations depend on the Axiom of Choice, hence are not unique, nevertheless they are unitarily equivalent to the classic Fock representation.