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Analyticity and the Global Information Field

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow, Russia
Academic Editor: Palle Jorgensen
Mathematics 2015, 3(1), 40-46; https://doi.org/10.3390/math3010040
Received: 10 February 2015 / Accepted: 9 March 2015 / Published: 13 March 2015
The relation between analyticity in mathematics and the concept of a global information field in physics is reviewed. Mathematics is complete in the complex plane only. In the complex plane, a very powerful tool appears—analyticity. According to this property, if an analytic function is known on the countable set of points having an accumulation point, then it is known everywhere. This mysterious property has profound consequences in quantum physics. Analyticity allows one to obtain asymptotic (approximate) results in terms of some singular points in the complex plane which accumulate all necessary data on a given process. As an example, slow atomic collisions are presented, where the cross-sections of inelastic transitions are determined by branch-points of the adiabatic energy surface at a complex internuclear distance. Common aspects of the non-local nature of analyticity and a recently introduced interpretation of classical electrodynamics and quantum physics as theories of a global information field are discussed. View Full-Text
Keywords: analyticity; asymptotic expansions; foundations of quantum physics analyticity; asymptotic expansions; foundations of quantum physics
MDPI and ACS Style

Solov'ev, E.A. Analyticity and the Global Information Field. Mathematics 2015, 3, 40-46.

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