[Paper Review] Decoherence: A dynamical approach to superselection rules?

Domenico Giulini|ArXiv.org|Oct 26, 2000

Quantum Mechanics and Applications35 references4 citations

TL;DR

This paper challenges the conventional distinction between 'hard' (symmetry-based) and 'soft' (decoherence-induced) superselection rules by arguing that even fundamental rules—like those for mass and electric charge—require dynamical input to be physically meaningful. It shows that decoherence mechanisms, particularly through infrared photon dressing in QED, can dynamically enforce superselection rules, suggesting that all superselection rules may ultimately arise from environmental interactions rather than being purely kinematical.

ABSTRACT

It is well known that the dynamical mechanism of decoherence may cause apparent superselection rules, like that of molecular chirality. These `environment-induced' or `soft' superselection rules may be contrasted with `hard' superselection rules, like that of electric charge, whose existence is usually rigorously demonstrated by means of certain symmetry principles. We address the question of whether this distinction between `hard' and `soft' is well founded and argue that, despite first appearance, it might not be. For this we give a detailed and somewhat pedagogical exposition of the basic structural properties of the spaces of states and observables in order to establish a fairly precise notion of superselection rules. We then discuss two examples: the Bargmann superselection rule for overall mass in ordinary quantum mechanics, and the superselection rule for charge in quantum electrodynamics.

Motivation & Objective

• To question the established dichotomy between 'hard' superselection rules (based on symmetries) and 'soft' ones (induced by decoherence).
• To investigate whether so-called 'hard' superselection rules actually depend on dynamical processes for physical justification.
• To analyze the role of decoherence in enforcing superselection rules in quantum electrodynamics (QED), particularly for electric charge.
• To explore whether the existence of superselection sectors for charge arises from physical limitations in state preparation, not just kinematical structure.
• To assess whether the infrared structure of QED—via photon dressing—provides a dynamical origin for superselection rules, resolving long-standing inconsistencies.

Proposed method

• Analyzes the Bargmann superselection rule for total mass in non-relativistic quantum mechanics as a model for kinematical superselection.
• Examines the charge superselection rule in QED through a heuristic treatment of the theory as a constrained Hamiltonian system.
• Applies the concept of environment-induced decoherence to show how phase relations between states with different momenta become locally inaccessible.
• Uses the retarded Coulomb field and flux distribution on a sphere to demonstrate that different momenta lead to distinct asymptotic field patterns.
• Introduces the infrared coherence condition of Zwanziger to show that coherent superpositions of charged particles require accompanying infrared photons.
• Demonstrates that the Gupta-Bleuler condition can be preserved in the infrared limit only when surface terms (asymptotic degrees of freedom) are included, preserving gauge invariance.

Experimental results

Research questions

• RQ1 Can 'hard' superselection rules, such as those for mass or charge, be understood as arising from dynamical processes rather than purely kinematical symmetries?
• RQ2 What physical mechanism prevents the coherent superposition of charged particles with different momenta in QED?
• RQ3 How does the inclusion of infrared photons (via the Zwanziger condition) restore coherence and resolve apparent inconsistencies with gauge invariance?
• RQ4 To what extent is the superselection structure in QED a consequence of decoherence due to long-range electromagnetic fields?
• RQ5 Can the distinction between 'hard' and 'soft' superselection rules be physically justified, or is it an artifact of formalism?

Key findings

• The superselection rule for electric charge in QED is not purely kinematical but emerges from the dynamical requirement of infrared consistency and the need to include asymptotic degrees of freedom.
• Coherent superpositions of charged particles with different momenta are only possible if they are dressed with appropriate infrared photons, which cancel their distinct asymptotic flux distributions.
• The infrared coherence condition of Zwanziger ensures compatibility with the Gupta-Bleuler transversality condition in the zero-frequency limit, resolving a long-standing inconsistency.
• Without inclusion of surface terms in the Hamiltonian, gauge invariance at spatial infinity cannot be maintained when charged states are included, implying that the superselection structure is dynamically enforced.
• The flux distribution of the retarded Coulomb field depends on the particle's momentum, leading to different asymptotic field patterns that define distinct superselection sectors.
• The distinction between 'hard' and 'soft' superselection rules is not physically robust, as even 'hard' rules like charge conservation rely on dynamical consistency conditions involving the infrared regime.