A reformulation of Hilbert's tenth problem through Quantum Mechanics

Abstract

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shrödinger propagator with some appropriate kernel. Either way, Mathematics and Physics could be combined for Hilbert's tenth problem and for the notion of effective computability.

References in corpus (3)

• Computable functions, quantum measurements, and quantum dynamics
• Computing the Noncomputable
• Numerical simulations of a quantum algorithm for Hilbert's tenth problem

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