Dirac Quantum Geometrodynamics

Russian Physics Journal - With the help of the Dirac procedure for extracting the root from the Hamiltonian operator of the free gravitational field in flat superspace-time, we have constructed a...     

Geometrodynamics in multidimensional unified theory

The unified theory of gravitation and a Yang-Mills field is formulated as a dynamical theory of (r+3)-geometries presumed to be principal bundles with Riemannian metric. Beyond the usual constraint equations the second fundamental form should satisfy a third constraint equation. It is shown that they have a wormhole type solution describing a pair of Yang-Mills charges.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Geometrodynamics vs. connection dynamics

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. We analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. We also couple varions matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. We derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, we construct constraint functions and analyze their Poisson bracket algebra. We demonstrate, whenever possible, equivalences between the theories.     

Geometrodynamics in Multidimensional Unified Theories

The unified theory of gravitation and a Yang-Mills field is formulated as a dynamical theory of (r+3) geometries presumed to be principal bundles endowed with a Riemannian metric. Beyond the usual constraint equations the second fundamental form should satisfy a third constraint equation. It is shown that they have a wormhole-type solution describing a pair of Yang-Mills charges.     

Quantum-Field Approach in Classical Physics and Geometrodynamics

Russian Physics Journal - A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multiparticle...     

Geometrodynamics for quarks and hadrons: The baryon states

In the geometrodynamical approach, baryons turn out to exist only in configuration where the quark coordinates are spatially aligned. As a consequence, the spectrum of [SU(6), L^P] multiplets follows the pattern: (56, 0⁺), (70, 1^?; (56, 2⁺), (70, 2⁺); (70, 3^?);… with their radial recurrences. This appears to solve an old quark-model puzzle.     

Geometrodynamics of electromagnetic fields in the Newman-Penrose formalism

The already unified field theory of Rainich, Misner, and Wheeler is rederived in the spin-coefficient formalism of Newman and Penrose. Conditions equivalent to the Rainich algebraic conditions are obtained by classifying the tracefree Ricci tensor according to its principal null directions. The case of a null electromagnetic field is also treated fully. Necessary and sufficient conditions are given for a Riemannian geometry to have an electromagnetic field, null or non-null, as its source.Supported in part by the National Research Council of Canada.     

Interpretation of Quantum Nonlocality by Conformal Quantum Geometrodynamics

The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl’s differential geometry are presented. The theory applied to the case of the relativistic single quantum spin \(\frac{1}{2}\) leads a novel and unconventional derivation of Dirac’s equation. The further extension of the theory to the case of two spins \(\frac{1}{2}\) in EPR entangled state and to the related violation of Bell’s inequalities leads, by a non relativistic analysis, to an insightful resolution of the enigma implied by quantum nonlocality.     

Quantum-Mechanical Problem with Periodic Initial Conditions in Classical Physics and Geometrodynamics

Russian Physics Journal - It is shown that in classical physics there is a time analog of a spatial quantum-mechanical problem with periodic boundary conditions. On this basis, it is shown that the...     

Quantum Solutions in Classical Electrodynamics and Its Connection with Geometrodynamics

Russian Physics Journal - A quantum solution of the classical electrodynamics equations has been found. It is shown that all information on the multiparticle process of creation of scalar pairs of...     

The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken.     

On a Relation Between the Bach Equation and the Equation of Geometrodynamics

The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation play the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of break geometrodynamics.     

Composite Topological Objects in Topological Superfluids

Journal of Experimental and Theoretical Physics - The spontaneous phase coherent precession of magnetization, discovered in 1984 by Borovik-Romanov, Bunkov, Dmitriev, and Mukharskiy [1] in...     

拓扑绝缘体及其研究进展

拓扑绝缘体是当前凝聚态物理领域中的一个热点问题.这类材料的典型特征是体内元激发存在能隙,但在边界上具有受拓扑保护的无能隙边缘激发.从广义上讲,拓扑绝缘体可以分两大类:一类是破坏时间反演的量子霍尔体系,另一类是新近发现的时间反演不变的拓扑绝缘体.这些新材料的奇特物理性质和潜在的应用前景,使其倍受人们关注.文章对这种新奇物态的物理性质和研究进展做了简要的介绍.     

Topological solitons

These are notes of the first part of the lectures on topological solitons, presented on Baikal Summer School on Physics of Elementary Particles and Astrophysics (July 2011). I review some of the basic properties of topological solitons on a simple model example of simple one-dimensional kink solution of the nonintegrable scalar ?⁴ model. I discuss both perturbative and non-perturbative sectors of the model, oscillon solution and resonance structures in the soliton collision.     

Topological Superfluids

Journal of Experimental and Theoretical Physics - There are many topological faces of the superfluid phases of 3He. These superfluids contain various topological defects and textures. The momentum...     

拓扑绝缘体及其研究进展

拓扑绝缘体是当前凝聚态物理领域中的一个热点问题.这类材料的典型特征是体内元激发存在能隙,但在边界上具有受拓扑保护的无能隙边缘激发.从广义上讲,拓扑绝缘体可以分两大类:一类是破坏时间反演的量子霍尔体系,另一类是新近发现的时间反演不变的拓扑绝缘体.这些新材料的奇特物理性质和潜在的应用前景,使其倍受人们关注.文章对这种新奇物态的物理性质和研究进展做了简要的介绍.     

Topological gravity

A version of conformal gravity is formulated with a local fermionic symmetry that is reminiscent of BRST invariance. It may have mathematical applications (gravitational counterpart of Donaldson theory) or physical ones (unbroken phase of general relativity).