Nonequivalent representations of nuclear algebras of canonical commutation relations. Quantum fields

TL;DR

This paper constructs explicit non-Fock representations of canonical commutation relations over nuclear spaces, demonstrating that different nuclear spaces lead to nonequivalent quantum field representations.

Contribution

It provides explicit constructions of non-Fock representations over nuclear spaces, highlighting the diversity of quantizations for scalar fields.

Findings

Explicit non-Fock representations constructed

Different nuclear spaces yield nonequivalent quantizations

Illustrates diversity in quantum field representations

Abstract

Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in nonequivalent quantizations of scalar fields.