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A. P. Kirilyuk
«Complex-Dynamic Solution to Many-Body Interaction Problem and Its Applications in Fundamental Physics»
217–280 (2012)

PACS numbers: 03.30.+p, 03.65.Ta, 03.67.-a, 05.45.-a, 05.65.+b, 11.10.Lm, 89.75.-k

We review the recently proposed irreducible complex-dynamic solving of the many-body problem with arbitrary interaction and its application to unified solving of fundamental problems, including dynamic foundations of causally complete quantum mechanics, relativity, particle properties, and cosmology. We first analyse the universal properties of many-body problem solution without any perturbative reduction and show that the emerging new quality of fundamental dynamic multivaluedness (or redundancy) of resulting system configuration leads to the natural and universal concept of dynamic complexity, chaoticity, and fractality of any real-system behaviour. We then consider unified features of such a complex dynamics and its main regimes of uniform (global) chaos and (multivalued) self-organisation as well as the dynamic nature of physically real space, irreversibly coursing time, and any system evolution in terms of its complexity conservation and transformation. Applications of that universal description to systems at various complexity levels have been performed, and, in a given paper, we review those at the lowest fundamental complexity levels leading to causal understanding of unified origins of quantum mechanics, (special and general) relativity, elementary particles, their intrinsic properties and interactions. Particularly, the complex-dynamic origin of inertial and gravitational (relativistic) masses is revealed without introduction of any additional particle species, fields, and dimensions. The related problem of ‘hierarchy’ of known particle masses (extreme values of Planck’s units) also acquires a parsimonious solution, leading to essential modification of high-energy physics research strategy. Other practically important consequences and problem solutions in fundamental physics and cosmology are summarised, confirming the efficiency of that unified picture based on complex-dynamic solution of irreducible many-body interaction problem.