Boris Rusakov

University of Minnesota - Twin Cities, Physics, Adjunct

Oxford university, Theoretical Physics, Emeritus

Tel Aviv University, School of Physics & Astronomy, Post-Doc

International Centre for Theoretical Physics (Trieste), High Energy Physics, Post-Doc

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PhD in Physics and Math from Academy of Sciences of USSR and Tomsk State University. Worked in Quantum Field Theory, Gauge theories, Quantum Chromodynamics, Group theory methods in QCD2. Current interests: AI, Consciousness, Human Mind, Information.

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Consciousness via Phase Transition of Learning: Qualia as a Property of Concepts

Building on recent advances in understanding of consciousness as constituted by a set of concepts... more Building on recent advances in understanding of consciousness as constituted by a set of concepts, this work proposes a formal description of this set as a space of consciousness. Geometrically, this is an N-dimensional vector space, where each of the N concepts corresponds to a basis vector. Algebraically, it is a space of N continuous functions, each corresponding to a concept. The concepts and the space of consciousness they constitute emerge via a phase transition of learning (or training) that is analogous to the discreteto-continuum transition (or clustering transition) in theoretical physics. A concept is a dual elementary entity that combines meaning and quale as its intrinsic properties. Qualia are therefore fundamental intrinsic properties of the space of consciousness and serve as mediators between the concepts and their physical substrates (neurons or neural networks). Since concepts emerge via learning, both their meanings and qualia can be modified through retraining. The role of correlators of concepts, or associations, is discussed. They are the reason for the non-Abelian character of information and therefore for the emergence and irreversibility of phenomenological time.

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Mathematical Philosophy of Consciousness: Towards Empirical and Theoretical study

Journal of Consciousness Exploration and Reasearch, 2024

Starting with previously introduced definition of information as a vector of concepts we extend i... more Starting with previously introduced definition of information as a vector of concepts we extend it to a matrix. The diagonal elements of the matrix are identical to the original concepts of the vector and represent pure reactions, while the off-diagonal elements are correlators of concepts and represent associations. While transformation of information within a particular nervous system occurs due to numerous internal (biological, psychological, behavioral, individual history, and etc.) factors we nevertheless can consider all these factors as a combined force acting on information and causing its change. Thus we define consciousness as a matrix operator acting on matrix of information. Under adiabatic approximation we derive a Schrodinger-type equation governing dynamics of consciousness and information. In equilibrium (calm, normal) state all new information falls into expected range. When deviation from equilibrium state exceeds some critical value the system becomes unstable (alert, concerned) and resolves the instability by creating a new concept, which is a phase transition. We also suggest that feelings correspond to a partial loss of consciousness and mathematically represented by off-equilibrium values of correlators of concepts.

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Concepts as Building Blocks of Information and The Structure of Consciousness

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Concepts as Building Blocks of Information and The Structure of Consciousness

We show that information, in contrast to the common belief, is not contained in a signal external... more We show that information, in contrast to the common belief, is not contained in a signal external to consciousness, but is a product of consciousness itself and is a set of concepts. The external signal serves as a trigger for the response of the nervous system. The response is subsequently analyzed by consciousness for its conceptual content. Information is a result of this analysis and can be considered a vector of concepts, i.e. conceptogram, of a signal for a specific consciousness at a specific moment. A concept is a sensory and visual image of a certain biochemical profile of the human nervous system, which is created and developed throughout one"s lifetime. It is an elementary building block of both human consciousness and information. In particular, "I" ("self") is one of the concepts. The creation of a particular concept is a phase transition. The Concept Module, or ability to generate concepts, is unique to humans. We offer scenarios for how this ability could have been acquired by our predecessors. It is suggested that the animal's brain, being a processor of visual signals that converts them into internal images, has developed this ability as a result of "guessing" or imagining details that are missing in the actual visible picture. We will also discuss some other issues related to consciousness that may be of interest to both Human and Artificial Intelligence research. Introduction: Concepts. Looking at an oak, birch, pine or willow, an animal does not try to understand what is common between them. It does not decide to call them all trees and does not look for what could be other trees. Humans do. You may correctly point out that, firstly, it is because animals do not have language. Secondly, they do not analyze, systemize, extract common properties, or look for reasons and explanation. But why do we do that while they do not? When did it start? Below, I hope I will answer these and some other questions.

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Loop Averages and Partition Functions in U(N) Gauge Theory on Two-Dimensional Manifolds

Modern Physics Letters A, 1990

Loop averages and partition functions in the U(N) gauge theory are calculated for loops without i... more Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including nonorientable ones. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities’ point of view, non-orientability of the manifold is equivalent to its non-compactness.

Lattice QCD as a theory of

Pure gauge lattice QCD at arbitrary D is considered. Exact integration over link variables in an ... more Pure gauge lattice QCD at arbitrary D is considered. Exact integration over link variables in an arbitrary D-volume leads naturally to an appearance of a set of surfaces filling the volume and gives an exact expression for functional of their boundaries. The interaction between each two surfaces is proportional to their common area and is realized by a non-local matrix differential operator acting on their boundaries. The surface self-interaction is given by the QCD 2 functional of boundary. Partition functions and observables (Wilson loop averages) are written as an averages over all configurations of an integer-valued field living on a surfaces.

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Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds

Mod.Phys.Lett.A 5 (1990) 693-703, 1990

Wilson loops in large N QCD on a sphere

Physics Letters B, 1994

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Ground state of 2D quantum gravity and spectral density of random matrices

Nuclear Physics B, 1993

We compute the exact spectral density of random matrices in the ground state of the quantum hamil... more We compute the exact spectral density of random matrices in the ground state of the quantum hamiltonian corresponding to the matrix model whose double scaling limit describes pure gravity in 2D. We show that the non-perturbative effects are very large and in certain cases dominate the semi-classical WKB contribution studied in the earlier literature. The physical observables in this model are the loop averages with respect to the spectral density. We compute their exact ground-state expectation values and show that they differ significantly from the values obtained in the WKB approximation. Unlike the alternative regularizations of the nonperturbative 2D quantum gravity, based on analytic continuation of the Painlevé transcendent, our solution shows no pathologies.

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Two-dimensional dynamics of QCD3

Physics Letters B, 1997

Exact loop-variables formulation of pure gauge lattice QCD 3 is derived from the Wilson version o... more Exact loop-variables formulation of pure gauge lattice QCD 3 is derived from the Wilson version of the model. The observation is made that the resulting model is two-dimensional. This significant feature is shown to be a unique property of the gauge field. The model is defined on the infinite genus surface which covers regularly the original three-dimensional lattice. Similar transformation applied to the principal chiral field model in two and three dimensions for comparison with QCD.

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Lattice QCD as a theory of interacting surfaces

Physics Letters B, 1995

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Exactly soluble QCD and confinement of quarks

Nuclear Physics B, 1997

An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling lim... more An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [1]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory.

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From hermitian matrix model to lattice gauge theory

I consider a lattice model of a gauge field interacting with matrix-valued scalars in $D$ dimensi... more I consider a lattice model of a gauge field interacting with matrix-valued scalars in $D$ dimensions. The model includes an adjustable parameter $\s$, which plays role of the string tension. In the limit $\s=\infty$ the model coincides with Kazakov-Migdal's ``induced QCD", where Wilson loops obey a zero area law. The limit $\s=0$, where Wilson loops $W(C)=1$ independently of the size of the loop, corresponds to the Hermitian matrix model. For $D=2$ and $D=3$ I show that the model obeys the same combinatorics as the standard LGT and therefore one may expect the area law behavior. In the strong coupling expansion such a behavior is demonstrated.

Large-N quantum gauge theories in two dimensions

Physics Letters B, 1993

The partition function of a two-dimensional quantum gauge theory in the large-N limit is expresse... more The partition function of a two-dimensional quantum gauge theory in the large-N limit is expressed as the functional integral over some scalar field. The large-N saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus g > 0. The existence of a nontrivial saddle point is closely related to the weak coupling behavior of the theory. Possible applications of the method to higher dimensions are briefly discussed.

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Wilson loops in large N QCD on a sphere

Physics Letters B - PHYS LETT B, 1994

Wilson loop averages of pure QCD at large N on a sphere are calculated by means of Makeenko-Migda... more

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Boris Rusakov

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