Kade Cicchella | Searcharxiv

arXiv2026

Scaling Limits as Extensions of Continuous Bundles of C*-algebras

We analyze scaling limits in algebraic quantum field theory using continuous bundles of C*-algebras. Different conditions of continuity on such bundles encode different strengths of approximation of the theory by its scaling limit. As a proof of concept, we consider the small-distance scaling limit of the theory of a massive free scalar field, which corresponds to a massless free scalar field. We provide a number of examples of local algebras of observables for which the corresponding bundle of C*-algebras representing the scaling limit is merely lower semicontinuous. Further, we construct an algebra of nonlocal observables for which the corresponding bundle of C*-algebras representing the scaling limit is uniformly continuous.

math-ph↗

arXiv2024

Quantum Probability via the Method of Arbitrary Functions

The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule probabilities can be derived from the unitary Schrödinger dynamics when certain dynamical parameters are treated as themselves random variables with initial probability distributions. Specifically, we study the perturbed double well model, in which the perturbation is treated as a random variable, and we show that for arbitrary initial distributions within a certain class, the dynamics yields the Born rule probabilities in the joint limits given by long times and small values of Planck's constant (the classical limit). Our results establish the Born rule as a type of universal limiting behavior that is independent of the precise initial dynamical parameters.

quant-ph↗