Unitarity Restoration for the Product of Nonunitary Operators

TL;DR

This paper proves that the polar decomposition method can restore unitarity when applied to products of invertible nonunitary operators, with implications for quantum propagators in spacetimes with closed timelike curves.

Contribution

It demonstrates the applicability of polar decomposition for unitarity restoration in complex operator products, extending previous theoretical frameworks.

Findings

Polar decomposition restores unitarity for nonunitary operator products.

Application to propagators in spacetimes with closed timelike curves.

Analogy with ghost introduction in gauge theories.

Abstract

A proof is given that the polar decomposition procedure for unitarity restoration works for products of invertible nonunitary operators. A brief discussion follows that the unitarity restoration procedure, applied to propagators in spacetimes containing closed timelike curves, is analogous to the original introduction by Feynman of ghosts to restore unitarity in non-abelian gauge theories. (The substance of this paper will be a note added in proof to the published version of gr-qc/9405058, to appear in Phys Rev D.)