The Rigged Hilbert Space Formulation of Quantum Mechanics and its Implications for Irreversibility

TL;DR

This paper explores how the Rigged Hilbert Space formulation of quantum mechanics provides a rigorous mathematical framework for describing quasistationary phenomena and reveals an intrinsic quantum arrow of time through Gamow vectors.

Contribution

It demonstrates that Gamow vectors exhibit microphysical irreversibility and derives an exact golden rule for decay transitions within this formalism.

Findings

Gamow vectors show intrinsic irreversibility.

The formalism introduces an intrinsic quantum arrow of time.

An exact golden rule for decay processes is derived.

Abstract

Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic quantum mechanical arrow of time, which states that preparation of a state has to precede the registration of an observable in this state. Moreover, the Rigged Hilbert Space formalism allows the derivation of an exact golden rule describing the transition of a pure Gamow state into a mixture of interaction-free decay products.