Вакуумное рождение частиц скалярного поля в конформно-инвариантной теории гравитации. Гамильтонов формализм и квантование релятивистских систем

model of gravitation in the frameworks of the Hamiltonian (Dirac) approach is considered. The equations, setting dependence of observable density of number of scalar particles on the initial data and invariant parametre of evolution, are constructed in an explicit form. Problems of unification of principles of the General Theory of Relativity (GTR) and the Quantum Theory of Fields (QTF) within a simple example of a vacuum creation of scalar particles in conformal-invariant model of gravitation [1-3,10-14] are considered. It is shown that such model can describe both possible mechanism of such creation, and ways of its generalisation to more complex models, including Standard Model (SM). It allows to formulate some new approach to quantization of the relativistic gravitational systems, which essence is in quantization of the phase space of initial quantities as integrals of motion of the system, obtained by Bogoljubov diagonalization of the motion equations in Hamiltonian formalism, and in the proof of equivalence of such quantization to transition from classical commutative variables to their noncommutative quantum analogues. The above described scheme can be applied to initial manifolds of any finite dimension and topology.В настоящей работе рассмотрена модель вакуумного рождения скалярных частиц в конформно-инвариантной модели гравитации в рамках гамильтонова (дираковского) подхода. Построены в явном виде уравнения, задающие в том числе зависимость наблюдаемой плотности числа частиц скалярного поля от начальных данных и инвариантного параметра эволюции. Рассмотрены проблемы объединения принципов общей теории относительности (ОТО) и квантовой теории поля (КТП) на простом примере вакуумного рождения скалярных частиц в конформно-инвариантной модели гравитации. Показано, что такая модель может описать как возможный механизм такого рождения, так и способы его обобщения на более сложные модели, в том числе и на Стандартную Модель (СМ). Сформулирован некоторый новый подход к квантованию релятивистских гравитирующих систем, суть которого заключается в квантовании фазового пространства начальных данных как интегралов движения системы, полученных путём Боголюбовской диагонализации уравнений гамильтонова формализма, и в доказательстве эквивалентности такого квантования переходу от классических пространственно-временных переменных к их некоммутирующим квантовым аналогам Вышеописанная схема может быть применена для исходного многообразия любой конечной мерности и топологии

Ферромагнетизм в графеновых и фуллереновых наноструктурах. Теория, моделирование, эксперимент

This work is devoted to the construction of the quantum field model, allowing, in particular, to describe ferromagnetic properties in graphen structures adequately to the results of physical and numerical experiments. The offered model describes properties of monoatom graphen layers ( forming two-dimensional surfaces), which are connected with presence of nontrivial function of distribution of the spin density, formed as a result of spontaneous breakdown of the spin symmetry of valent electrons in atoms of carbon. Within the limits of the offered model possible exact solutions for field function of the spin density, explaining, in particular, experimentally observed ferromagnetic properties of graphen films are specified. Quantitative estimations of a thickness of the domain wall, dividing areas with counterdirected vectors of magnetization were suggested, which allows to check up offered theoretical model experimentally.Работа посвящена построению квантовополевой модели, позволяющей, в частности, описывать ферромагнитные свойства в графеновых структурах адекватно имеющимся физическим и численным результатам. Предлагается модель, описывающая такие свойства графеновых моноатомных слоёв, образующих двумерные поверхности, которые связаны с наличием нетривиальной функции распределения спиновой плотности, образованной в результате спонтанного нарушения спиновой симметрии валентных электронов атомов углерода на указанных поверхностях. В рамках предлагаемой модели указываются возможные точные решения для функции спиновой плотности, объясняющие, в частности, экспериментально наблюдаемые ферромагнитные свойства графеновых плёнок. Делаются количественные оценки толщины доменной стенки, разделяющей области с разнонаправленной намагниченностью, позволяющие экспериментально проверить предлагаемую теоретическую модель

A consequence of applying the generalized permutation relations in quantum theory of interacting fields

In this paper, we examine a generalization of the permutation relations, used In quantum theory of fields, which ensure satisfaction of the basic physical requirements imposed on the interaction matrix in the case being examined. In this generalization, the cross section for scattering of a vector massless particle by a spinor particle is calculated. It is shown that here, in particular, the probability for the appearance of unphysical ("time-like" and "longitudinal") vector particles as a result of scattering may be made to vanish. © 1982 Plenum Publishing Corporation

A consequence of applying the generalized permutation relations in quantum theory of interacting fields

In this paper, we examine a generalization of the permutation relations, used In quantum theory of fields, which ensure satisfaction of the basic physical requirements imposed on the interaction matrix in the case being examined. In this generalization, the cross section for scattering of a vector massless particle by a spinor particle is calculated. It is shown that here, in particular, the probability for the appearance of unphysical ("time-like" and "longitudinal") vector particles as a result of scattering may be made to vanish. © 1982 Plenum Publishing Corporation

Method for generation spin waves

In the method, a pre-selected working area of a graphene film with a linear dimension of 2,000 nm, which working area is divided into sections having a dimension of 50-100 nm, is subjected to the effect of a pulsed alternating magnetic field with a frequency of 3 terahertz that corresponds to the transition from the ground energy level, corresponding to the non-excited state of spin density, to a fourth working energy level of the excited state of spin density in the graphene film, thus causing spin density pumping. A spatially localized external magnetic field is generated around the edges of the working area, which resonantly reflects spinons having a working frequency of 0.5-1 terahertz that corresponds to the transition from a third working energy level to a second working energy level of the excited state of spin density, said spinons causing the induced coherent radiation of working frequency spin waves as they pass thorough the working area. Патент США, класс 324/300

NONLINEAR SPIN WAVES IN GRAPHENE STRUCTURES

Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron-electron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kink-antikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and, finally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Possible inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can find practical applications in nanoelectronics and spintronics

Model for spin waves and lasing in monolayer graphene films

Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron-electron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kink-antikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and, finally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Once created, the inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can find practical applications in nanoelectronics and spintronics. Optical excitation and possible lasing transitions between the breather discrete states are discussed. © 2015 SPIE

NONLINEAR SPIN WAVES IN GRAPHENE STRUCTURES

Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron-electron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kink-antikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and, finally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Possible inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can find practical applications in nanoelectronics and spintronics