arXiv subjects

G. N. Parfionov

Publications and source records attributed to G. N. Parfionov.

9 recordsLinked to original sources

arXiv2008

How to play macroscopic quantum game

Quantum games are usually considered as games with strategies defined not by the standard Kolmogorovian probabilistic measure but by the probability amplitude used in quantum physics. The reason for the use of the probability amplitude or "quantum probabilistic measure", is the nondistributive lattice occurring in physical situations with quantum microparticles. In our paper we give examples of getting nondistributive orthomodular lattices in some special macroscopic situations without use of quantum microparticles.

quant-ph↗

arXiv2005

Distributivity breaking and macroscopic quantum games

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for the use of the quantum formalism is in breaking of the distributivity property for the lattice of yes-no questions arising due to the special rules of games. The rules of the games suppose two parts: the preparation and measurement. In the first part due to use of the quantum logical orthocomplemented non-distributive lattice the partners freely choose the wave functions as descriptions of their strategies. The second part consists of classical games described by Boolean sublattices of the initial non-Boolean lattice with same strategies which were chosen in the first part. Examples of games for spin one half are given. New Nash equilibria are found for some cases. Heisenberg uncertainty relations without the Planck constant are written for the "spin one half game".

quant-ph↗

arXiv2005

When the macroscopic game is the quantum game?

An example of the macroscopic game of two partners consisting of two classical games played simultaneously with special dependence of strategies is considered. The average profit of each partner is equal to the average profit obtained in the quantum game with two noncommuting operators for the spin one half system with strategies defined by the wave function. Nash equilibria in the macroscopic game coincide with Nash equilibria of the quantum game.

quant-ph↗

arXiv1999

Topology measurement within the histories approach

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretised spacetime models is established.

quant-ph↗

arXiv1998

Connes duality in Lorentzian geometry

The Connes formula giving the dual description for the distance between points of a Riemannian manifold is extended to the Lorentzian case. It resulted that its validity essentially depends on the global structure of spacetime. The duality principle classifying spacetimes is introduced. The algebraic account of the theory is suggested as a framework for quantization along the lines proposed by Connes. The physical interpretation of the obtained results is discussed.

gr-qc↗

arXiv1997

Empirical topology in the histories approach to quantum theory

An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretized spacetime models is established.

gr-qc↗

arXiv1995

Vectors and covectors in non-commutative setting

Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

q-alg↗

arXiv1995

POINTLESS SPACES IN GENERAL RELATIVITY

The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise to points by loosing a part of the entire structure is discussed. The counterpart of the traditional objects of differential geometry are studied.

gr-qc↗

arXiv1995

Dual Structures in Non-Commutative Differential Algebras

The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is introduced and the conditions for appropriate moduli to be reflexive are obtained.

q-alg↗