0 Classical and quantum mechanics on information spaces with applications to cognitive , psychological , social and anomalous phenomena

Classical and quantum dynamics on p-adic trees of ideas.

We propose mathematical models of information processes of unconscious and conscious thinking (based on p-adic number representation of mental spaces). Unconscious thinking is described by classical cognitive mechanics (which generalizes Newton's mechanics). Conscious thinking is described by quantum cognitive mechanics (which generalizes the pilot wave model of quantum mechanics). The informat...

Quantum-like model of processing of information in the brain based on classical electromagnetic field

We propose a model of quantum-like (QL) processing of mental information. This model is based on quantum information theory. However, in contrast to models of "quantum physical brain" reducing mental activity (at least at the highest level) to quantum physical phenomena in the brain, our model matches well with the basic neuronal paradigm of the cognitive science. QL information processing is b...

Noncommutative geometry and number theory

Noncommutative geometry is a modern field of mathematics begun by Alain Connes in the early 1980s. It provides powerful tools to treat spaces that are essentially of a quantum nature. Unlike the case of ordinary spaces, their algebraof coordinates is noncommutative, reflecting phenomena like the Heisenberg uncertainty principle in quantum mechanics. What is especially interesting is the fact th...

A new class of function spaces on domains of R^d and its relations to classical function spaces

A Correspondence Principle

A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical “correspondence principle”, a kind of wave–particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative case...