Does decoherence violate decoupling? (2411.09000v1)

Abstract: Recent calculations in both flat and de Sitter spacetimes have highlighted a tension between the decoupling of high-energy physics from low-energy degrees of freedom and the expectation that quantum systems decohere due to interactions with unknown environments. In effective field theory (EFT), integrating out heavy fields should lead to Hamiltonian time evolution, which preserves the purity of low-energy states. This is consistent with the fact that we never observe isolated quantum states spontaneously decohering in the vacuum due to unknown high-energy physics. However, when a heavy scalar of mass $M$ is traced out, the resulting purity of a light scalar with mass $m$ typically appears to scale as a power of $1/M$ (when $m\ll M$), an effect that cannot be captured by a local effective Hamiltonian. We resolve this apparent paradox by showing that the purity depends on the resolution scale of the EFT and how the environment is traced out. We provide a practical method for diagnosing the purity of low-energy states consistent with EFT expectations, and briefly discuss some of the implications these observations have for how ultraviolet divergences can appear in decoherence calculations.

• The paper investigates an apparent tension where decoherence effects seem to scale inversely with the mass of integrated-out high-energy fields, seemingly violating decoupling in Effective Field Theory (EFT).
• It demonstrates that this apparent violation is resolved by carefully considering the EFT resolution scale and how the environment is traced out, reconciling decoherence effects with decoupling expectations.
• The study highlights the crucial role of the i The paper investigates an apparent tension where decoherence effects seem to scale inversely with the mass of integrated-out high-energy fields, seemingly violating decoupling in Effective Field Theory (EFT).
• It demonstrates that this apparent violation is resolved by carefully considering the EFT resolution scale and how the environment is traced out, reconciling decoherence effects with decoupling expectations.
• The study highlights the crucial role of the i\epsilon prescription in ensuring that environmental projection correctly accounts for expected decoupling effects in open quantum systems.

Overview of "Does decoherence violate decoupling?"

The paper "Does decoherence violate decoupling?" by Burgess, Colas, Holman, and Kaplanek investigates the interplay between decoherence and decoupling within the framework of Effective Field Theory (EFT). The authors explore the tension that arises in quantum field theories when high-energy physics is integrated out to deliver a low-energy approximation. Specifically, the paper explores how decoherence effects manifest, even when ultraviolet (UV) physics supposedly decouples from infrared (IR) phenomena.

Key Findings and Results

1. Decoupling and Decoherence: The authors begin by exploring the typical expectation in EFT that high-energy (UV) degrees of freedom should decouple from low-energy (IR) physics. In essence, integrating out heavy fields should, in principle, lead to Hamiltonian evolution at low energies, a process that preserves the purity of quantum states. However, explicit calculations in the paper seem to indicate an apparent violation of this expectation, presenting scenarios where decoherence appears to scale inversely with the mass of integrated-out fields.
2. Resolution of the Paradox: By closely examining the mathematical frameworks of decoherence and decoupling, the authors demonstrate that apparent decoherence effects stemming from heavy physics can be reconciled with decoupling through careful treatment of EFT's resolution scale. They argue that the decoherence observed is contingent on how the environment is traced out, and thus not inherent to violating decoupling.
3. Purity Calculations: The purity of quantum states is used as a metric to gauge decoherence. In several worked examples involving scalar fields with differing interaction terms, they illustrate how decoherence effects emerge when heavy fields are integrated out. Despite apparent decoherence at finite orders, when analyzed correctly with the appropriate resolution scale, these effects align with the theoretical framework of EFT that should suppress them.
4. Role of the $\epsilon$-Prescriptions: A critical insight from the paper is the role of the $i\epsilon$ prescription in EFT calculations. The authors show that ensuring negative imaginary components in time differences within Wightman functions enforces the proper environmental projection, automatically accounting for the decoupling effects expected in EFT. This ensures that decoherence does not misrepresent UV effects at low energies.

Theoretical and Practical Implications

The research encapsulated in this paper carries significant implications for both the formal development of quantum field theory and practical computational strategies:

• Theoretical Insight into EFT: The paper refines the understanding of how EFT should be understood when considering open quantum systems. The insights provided motivate the need to clearly delineate the influence of UV physics when considering quantum decoherence.
• Computational Practices: Practically, the findings inform more accurate computational practices. Understanding when and how heavy fields contribute to decoherence is vital for constructing low-energy effective Hamiltonians that do not erroneously predict the decoherence of states.
• Future Directions in Adiabatic and Cosmological Settings: The work points the way to more nuanced studies of open quantum systems, particularly within cosmological contexts where the time evolution of states and the adiabatic assumptions of EFT are continually tested. The discussion on UV divergences hints at potential further exploration in UV completions and renormalization practices for open EFTs.

Conclusion

In summary, this paper cuts through a theoretical puzzle about the interaction between decoherence and decoupling in quantum systems, ultimately reinforcing the robustness of EFT when analyzed with precision. The insights gained offer guidance for more effective modeling of quantum systems, particularly in settings where the pristine assumptions of closed systems do not hold.