Uploaded September 2024 | Updated September 2026, 2 weeks ago
Title: The Aim and Structure of Cluster Decomposition
Abstract:
The architecture of quantum field theory includes a handful of load-bearing locality or causality conditions. One of the most important is the cluster decomposition property: roughly speaking, a property intended to capture the fact that the outcome of experiments at Fermilab is independent of whatever might be happening in the accelerator tunnel at SLAC. Steven Weinberg went so far as to call it a foundational requirement of all experimental science. However, the statistical independence required by cluster decomposition is in tension with the long-range correlations characteristic of entangled states. Nevertheless, something very much like Weinberg’s transcendental-ish claim is probably correct but appreciating that requires disentangling the role of the cluster decomposition property from its standard mathematical presentation and elucidating a delicate relationship between the cluster decomposition property and the ubiquity of entanglement in quantum field theory.
Title: The Aim and Structure of Cluster Decomposition
Abstract:
The architecture of quantum field theory includes a handful of load-bearing locality or causality conditions. One of the most important is the cluster decomposition property: roughly speaking, a property intended to capture the fact that the outcome of experiments at Fermilab is independent of whatever might be happening in the accelerator tunnel at SLAC. Steven Weinberg went so far as to call it a foundational requirement of all experimental science. However, the statistical independence required by cluster decomposition is in tension with the long-range correlations characteristic of entangled states. Nevertheless, something very much like Weinberg’s transcendental-ish claim is probably correct but appreciating that requires disentangling the role of the cluster decomposition property from its standard mathematical presentation and elucidating a delicate relationship between the cluster decomposition property and the ubiquity of entanglement in quantum field theory.
