Creation And Annihilation Research Articles

Fatou's theorem for non-commutative measures

A classical theorem of Fatou asserts that the Radon–Nikodym derivative of any finite and positive Borel measure, μ, with respect to Lebesgue measure on the complex unit circle, is recovered as the non-tangential limits of its Poisson transform in the complex unit disk. This positive harmonic Poisson transform is the real part of an analytic function whose Taylor coefficients are in fixed proportion to the conjugate moments of μ.Replacing Taylor series in one variable by power series in several non-commuting variables, we show that Fatou's Theorem and related results have natural extensions to the setting of positive harmonic functions in an open unit ball of several non-commuting matrix-variables, and a corresponding class of positive non-commutative (NC) measures. Here, an NC measure is any positive linear functional on a certain self-adjoint unital subspace of the Cuntz–Toeplitz algebra, the C⁎−algebra generated by the left creation operators on the full Fock space.

The anisotropic Dunkl oscillator problem on the two-dimensional curved spaces

In this paper, we study the two-dimensional (2D) Euclidean anisotropic Dunkl oscillator model in an integrable generalization to curved ones of the 2D sphere [Formula: see text] and the hyperbolic plane [Formula: see text]. This generalized model depends on the deformation parameter [Formula: see text] of underlying space and involves reflection operators [Formula: see text] in such a way that all the results are simultaneously valid for [Formula: see text], [Formula: see text] and [Formula: see text]. It turns out that this system is superintegrable based on the special cases of parameter [Formula: see text], which constant measures the asymmetry of the two frequencies in the 2D Dunkl model. Therefore, the Hamiltonian [Formula: see text] can be interpreted as an anisotropic generalization of the curved Higgs–Dunkl oscillator in the limit [Formula: see text]. When [Formula: see text], the system turns out to be the well-known superintegrable 1:2 Dunkl oscillator on [Formula: see text] and [Formula: see text]. In this way, the integrals of the motion arising from the anisotropic Dunkl oscillator are quadratic in the Dunkl derivatives for the special cases of [Formula: see text]. Moreover, these symmetries obtain by the Jordan–Schwinger representation in the family of the Cayley–Klein orthogonal algebras using the creation and annihilation operators of the dynamical [Formula: see text] algebra of the 1D Dunkl oscillator. The resulting algebra is a deformation of [Formula: see text] with reflections, which is named the Jordan–Schwinger–Dunkl algebra [Formula: see text]. The spectrum of this system is determined by the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

Change of business models of Ukrainian insurance companies in the conditions of COVID-19

Insurance companies form their own business models based on the interests of stakeholders. Changes in business models are due to the impact of COVID-19, deepening digitalization and customer orientation. Accordingly, the aim of the study is to systematize the approaches to business models of insurance companies using emerging market country (Ukraine) as an example, and to show the change in a business model according to the CANVAS approach under the influence pandemic. In accordance with the purpose of the study, business models of insurance companies were systematized and grouped into blocks: value-based, structural, complex, and strategic. The strategic block identifies strategic changes in the activities of insurance companies and reflects trends on the insurance market. With this in mind, business models of insurance companies should reflect the set of strategic decisions, their architecture, structure and facilitate the management of value creation operations on the insurance market. Business models have changed from traditional to innovative, hybrid and digital-oriented. The main changes in the business models of insurance companies are omnichannel communications, the launch of chatbots, Big Data, Mobile ID, Bank ID, online access to registers, Blockchain. The COVID-19 pandemic has led to a shift in business models towards socially responsible business and adherence to sustainable development goals.

СВІТОВІ ТРЕНДИ «ЗЕЛЕНОГО» ІНВЕСТУВАННЯ

The article is devoted to the study of the main current trends of green investment, as well as to substantiate the prospects for development in the context of the globalization of the "green" movement. It was revealed that the key global trends are the creation and successful operation of specialized sectors of "green" bonds on world exchanges and their labeling to attract non-global investors to the market. The article identifies the main sectors for the use of "green" bonds, namely renewable energy sources, energy efficiency, pollution prevention, clean transport, water resources and wastewater management, adaptation to climate change. The author argues that the promotion of "green" projects and the development of responsible investment markets are the most important factors in the world economy, so the implementation of environmental reforms at the state level should be associated with the development of "green" financing instruments. The article identifies global drivers that necessitate the formation of an adequate institutional environment for the current realities for the development of "green" funding; systematizes the world experience of "green" investment and identifies effective tools for financing "green" projects. The author notes that it is important to overcome political, methodological, regulatory and economic contradictions in the formation of common rules of "green" development between developed and developing countries. It is determined that further development of "green" financing is impossible without systematic, planned and coordinated institutional design of a multilevel system of different financial instruments, taking into account the characteristics of different types of investors, their incentives to implement "green" projects and potential implementation effects. The standardization of approaches and methodological principles that allow to evaluate the effectiveness of environmental projects, the development of practical goals in the field of a wide range of "green" financial products are identified as promising areas of further research.

A Way to Quantum Gravity

We present a simple way to approach the hard problem of quantization of the gravitational field in four-dimensional space-time, due to non-linearity of the Einstein equations. The difficulty may be overcome when the cosmological constant is non-null. Treating the cosmological contribution as the energy-momentum of vacuum, and representing the metric tensor onto the tetrad of its eigenvectors, the corresponding energy-momentum and, consequently, the Hamiltonian are easily quantized assuming a correspondence rule according to which the eigenvectors are replaced by creation and annihilation operators for the gravitational field. So the geometric Einstein tensor, which is opposite in sign respect to the vacuum energy-momentum (plus the possible known matter one), is also quantized. Physical examples provided by Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter solutions are examined.

ВИЩИЙ СУД З ПИТАНЬ ІНТЕЛЕКТУАЛЬНОЇ ВЛАСНОСТІ: ПРОБЛЕМИ ТА ПЕРСПЕКТИВИ ДІЯЛЬНОСТІ

The article examines the features of the protection of intellectual property rights, taking into account the formation in Ukraine of a specialized judicial body for the consideration and resolution of disputes in this area – the Supreme Court for Intellectual Property. The publication analyzes the characteristics and difficulties of litigation and dispute resolution in the field of intellectual property, contradictions with the current legislation of Ukraine governing relations of intellectual activity, organizational issues, problems and prospects for the activities of the Supreme Court on intellectual property issues, formulates conclusions on improving the system of legal protection of intellectual property. In the process of studying the features and prospects of the activities of the Supreme Court on intellectual property issues, general scientific and special legal methods were used, in particular, dialectical, formal-logical, historical, normative-comparative, systemic-structural, etc. Based on consideration of the features of protecting intellectual property rights in court, assessing the problem and determining the prospects for the activities of a specialized court for the consideration and resolution of disputes in the field of intellectual property – the Supreme Court on Intellectual Property, it was concluded that at present the necessary legislative framework has been formed in Ukraine, which would ensure the implementation and guarantee of compliance with the rights to the results of intellectual, creative activity. However, the complexity of adjudication of disputes in the field of intellectual property, their duration, the lack of generalized judicial practice – these factors negatively affect the level of legal protection of intellectual property subjects. The solution of these problems should ensure the functioning of the Supreme Court for Intellectual Property, the creation and effective operation of which will significantly increase the level of protection of the rights of intellectual property subjects.

Industry 4.0 for sustainable supply chain management: Drivers and barriers

Sustainable supply chain management is one of the greatest challenges for the competitive, environmental and social performance of the industry, finding in the technological applications of Industry 4.0 mechanisms that drive its development. This study recognizes the aspects that determine the application of Industry 4.0, for the sustainability of the supply chain at multiple levels. To do so, the study conducts a bibliometric analysis and systematic literature review, based on 249 academic papers, which are thematically analyzed and categorized in terms of barriers, limitations, and benefits, applying the PRISMA systematic research protocol. The results suggest that environmental, economic and social concerns, as well as operational, technological, competitive, environmental and social benefits, together with drivers such as digital infrastructure financing, public and private support structures and the existence of a legal and political framework and government intervention allow the creation and sustained operation of sustainable supply chains. However, inefficient organizational culture and policies, manifested in the lack of awareness of employees and actors in the chain, the low level of transparency, security and cooperation in the use of data, high research and development costs, limited organizational resources, inadequate public policies and lack of financial support are aspects that inhibit their proper implementation.

Higher Order Self-Induced Self-Interacting Field

The genesis of physical particles is essentially a mystery. Quantum field theory creation operators provide an abstract mechanism by which particles come into existence, but quantum fields do not possess energy density. I reference several recent treatments of this problem and develop ideas based on self-stabilizing field structures with focus on higher order self-induced self-stabilizing field structures. I extend this treatment in this paper to related issues of topological charge.

Particle Creation from Yang-Mills Gravity

The genesis of physical particles, a foundational aspect of physics, is still a mystery. Quantum field theory creation operators provide an abstract mechanism to bring particles into existence. The assumption of a primordial field underlies the Standard Model (SM), yet the forces have failed to converge to such a field. Current treatments of a superfluid-based universe [Huang, Volovik, and Svistunov, Babaev, Prokof’ev] focus heavily on vortices and Yang-Mills theory, so we analyze self-interaction of the primordial field in the context of Yang-Mills. We show that a self-stabilizing higher-order self-interaction interpretation of the Yang-Mills non-Abelian term yields a stable quantum gravity explanation of the mass-gap. In future we will address the and conserved charge aspects in terms of this fundamental theory of particle creation.

Integrality, duality and finiteness in combinatoric topological strings

A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension dR of any irreducible complex representation of G. We show that the integer ratios {left|Gright|}^2/{d}_R^2 are combinatorially constructible using finite algorithms which take as input the amplitudes of combinatoric topological strings (G-CTST) of finite groups based on 2D Dijkgraaf-Witten topological field theories (G-TQFT2). The ratios are also shown to be eigenvalues of handle creation operators in G-TQFT2/G-CTST. These strings have recently been discussed as toy models of wormholes and baby universes by Marolf and Maxfield, and Gardiner and Megas. Boundary amplitudes of the G-TQFT2/G-CTST provide algorithms for combinatoric constructions of normalized characters. Stringy S-duality for closed G-CTST gives a dual expansion generated by disconnected entangled surfaces. There are universal relations between G-TQFT2 amplitudes due to the finiteness of the number K of conjugacy classes. These relations can be labelled by Young diagrams and are captured by null states in an inner product constructed by coupling the G-TQFT2 to a universal TQFT2 based on symmetric group algebras. We discuss the scenario of a 3D holographic dual for this coupled theory and the implications of the scenario for the factorization puzzle of 2D/3D holography raised by wormholes in 3D.

Dirac oscillator in dynamical noncommutative space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by a dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in the dynamical noncommutative space, in which the space-space Heisenberg-like commutation relations and noncommutative parameter are position-dependent. Then, we used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the language of creation and annihilation operators and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that, with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

The q-analogue of the Higgs algebra

In this paper, the q-generalization of the Higgs algebra is considered. The realization of this algebra is shown in an explicit form using a nonlinear transformation of the creation-annihilation operators of the q-harmonic oscillator. This transformation is the performance of two operations, namely, a “correction” using a function of the original Hamiltonian, and raising to the fourth power the creation and annihilation operators of a q-harmonic oscillator. The choice of the “correcting” function is justified by the standard form of commutation relations for the operators of the metaplectic realization Uq(SU(1,1)). Further possible directions of research are briefly discussed to summarize the results obtained. The first direction is quite obvious. It is the consideration of the problem when the dimension of the operator space increases or for any value N. The second direction can be associated with the analysis of the relationship between q-generalizations of the Higgs and Hahn algebras.

Statistical model describing Bose-Einstein and Fermi-Dirac statistics.

Beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles, a unified quantum statistics, which may interpolate smoothly between Bose-Einstein and Fermi-Dirac statistics, is proposed. The commutation relations for such particle creation and annihilation operators are derived, and statistical partition function and thermodynamical properties of an ideal gas of the particles are investigated. Besides the Bose-Einstein condensation, another kind of particle condensation may appear.

Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence

Quantisation of Lorentz invariant scalar field theory in Doplicher-Fredenhagen-Roberts (DFR) space-time, a Lorentz invariant, non-commutative space-time is studied. We use an approach to quantisation that is based on the equations of motion alone and derive the equal time commutation relation between Doplicher-Fredenhagen-Roberts-Amorim (DFRA) scalar field and its conjugate, which has non-commutative dependent modifications, but the corresponding creation and annihilation operators obey usual algebra. We show that imposing the condition that the commutation relation between the field and its conjugate is same as that in the commutative space-time leads to a deformation of the algebra of quantised oscillators. Both these deformed commutation relations derived are valid to all orders in the non-commutative parameter. By analysing the first non-vanishing terms which are θ3 order, we show that the deformed commutation relations scale as 1/λ4, where λ is the length scale set by the non-commutativity of the space-time. We also derive the conserved currents for DFRA scalar field. Further, we analyse the effects of non-commutativity on Unruh effect by analysing a detector coupled to the DFRA scalar field, showing that the Unruh temperature is not modified but the thermal radiation seen by the accelerated observer gets correction due to the non-commutativity of space-time.

Creation and Combat Operations of Fighter-Sabotage Detachments of the Black Sea Group of Troops during the Second World War

Creation and Combat Operations of Fighter-Sabotage Detachments of the Black Sea Group of Troops during the Second World War

Singular value decomposition for skew-Takagi factorization with quantum applications

We obtain an algorithm for the skew-Takagi factorization based on the singular value decomposition. As an example application of such an algorithm, we consider the computation of Heisenberg evolution of the fermionic creation and annihilation operators in the case of the quadratic Hamiltonian of a special form

Spectrum of the semi-relativistic Pauli–Fierz model II

We consider the ground state of the semi-relativistic Pauli–Fierz Hamiltonian $$ H = |\textbf{p} - \textbf{A(x)}| + H\_f + V\textbf{(x)}. $$ Here $\textbf{A(x)}$ denotes the quantized radiation field with an ultraviolet cutoff function and $H\_f$ the free field Hamiltonian with dispersion relation $|\textbf{k}|$. The Hamiltonian $H$ describes the dynamics of a massless and semi-relativistic charged particle interacting with the quantized radiation field with an ultraviolet cutoff function. In 2016, the first two authors proved the existence of the ground state $\Phi\_m$ of the massive Hamiltonian $H\_m$ is proven. Here, the massive Hamiltonian $H\_m$ is defined by $H$ with dispersion relation $\sqrt{\textbf{k}^2+m^2}$ $(m>0)$. In this paper, the existence of the ground state of $H$ is proven. To this aim, we estimate a singular and non-local pull-through formula and show the equicontinuity of ${a(k)\Phi\_m}{0\<m\<m\_0}$ with some $m\_0$, where $a(k)$ denotes the formal kernel of the annihilation operator. Showing the compactness of the set ${\Phi\_m}{0\<m\<m\_0}$, the existence of the ground state of $H$ is shown.

Second Quantization Approach to COVID-19 Epidemic

In this article, a stochastic SIR-type model for COVID-19 epidemic is built using the standard field theoretical language based on creation and annihilation operators. From the model, we derive the time evolution of the mean number of infectious (active cases) and deceased individuals. In order to capture the effects of lockdown and social distancing, we use a time-dependent infection rate. The results are in good agreement with the data for three different waves of epidemic activity in South Korea.

Seesaw, coherence and neutrino oscillations

We present a prescription for consistently constructing non-Fock coherent flavour neutrino states within the framework of the seesaw mechanism, and establish that the physical vacuum of massive neutrinos is a condensate of Standard Model massless neutrino states. The coherent states, involving a finite number of massive states, are derived by constructing their creation operator. This construction fulfills automatically the key requirement of coherence for the oscillations of particles to occur. We comment on the inherent non-unitarity of the oscillation probability induced by the requirement of coherence.

Annihilation operators for exponential spaces in subdivision

We investigate properties of differential and difference operators annihilating certain finite-dimensional spaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this technical note comes from considering subdivision schemes where annihilation operators play an important role. Indeed, subdivision schemes with the capability of preserving exponential functions can be used to obtain an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions, and annihilation operators are useful to automatically detect the frequencies of such functions.