A reformulation of Hilbert's tenth problem through Quantum Mechanics

Details A reformulation of Hilbert's tenth problem through Quantum Mechanics A reformulation of Hilbert's tenth problem through Quantum Mechanics

2001-11-12

arxiv.org/abs/quant-ph/0111063v2

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

Physics

Quantum Physics

Scientific paper

10.1098/rspa.2003.1266

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 Shr\"odinger 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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