A reformulation of Hilbert's tenth problem through Quantum Mechanics

2001/11/30 by Tien D Kieu
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1098/rspa.2003.1266

published as Proc Roy Soc A 460 (2004) 1535 (Final version with modifications)

arxiv created 2003/10/08 · arxiv updated 2009/12/01

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.

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