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While a classical bit found in conventional electronics exists only in binary one or zero states, the more resourceful quantum bit, or ‘qubit,’ is represented by a vector, pointing to a simultaneous c...
EUGENE, Ore. — (March 20, 2014) — University of Oregon physicists using a supercomputer and mathematically rich formulas have captured fundamental insights about what happens when objects moving freel...
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are relate...
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions.
Abstract: We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After revi...
Abstract: It is shown that for each finite number of Dirac measures supported at points $s_n$ in three-dimensional Euclidean space, with given amplitudes $a_n$, there exists a unique real-valued Lipsc...
Abstract: We review and further analyze Penrose's 'light cone at infinity' - the conformal closure of Minkowski space. Examples of a potential confusion in the existing literature about it's geometry ...
Abstract: We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalou...
Abstract: We consider generalizations of symplectic manifolds called n-plectic manifolds. A manifold is n-plectic if it is equipped with a closed, nondegenerate form of degree n+1. We show that higher...
Abstract: A physical interpretation of the two-sheeted space, the most fundamental ingredient of noncommutative spectral geometry proposed by Connes as an approach to unification, is presented. It is ...
Abstract: We present a study of the Dirac theory of constraints emphasizing the duality between the Poisson-algebraic and the geometric points of view, related respectively to the work of Dirac and of...
Abstract: A sketch of an approach towards Lorentzian spectral geometry (based on joint work with Mario Paschke) is described, together with a general way to define abstractly the quantized Dirac field...

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