相关论文: Physical Vacuum Properties and Internal Space Dime…

The use in the action integral of a volume element of the form $\Phi d^{D}x$ where $\Phi$ is a metric independent measure can give new interesting results in all types of known generally coordinate invariant theories: (1) 4-D theories of…

The integrability of two symplectic maps, that can be considered as discrete-time analogs of the Garnier and Neumann systems is established in the framework of the $r$-matrix approach, starting from their Lax representation. In contrast…

Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have…

In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the…

A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…

Vacuum, where matter exists is an objective reality of Nature. It has a structure consists of electrical massless dipoles. This structure is responsible for gravitation, inertia and propagation of light. The structure can be influenced by…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this…

We consider multidimensional cosmological models with a generalized space-time manifold M = R x M_1 ...x M_n, composed from a finite number of factor spaces M_i, i=1,..n. While usually each factor space M_i is considered to be some…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional…

Mass is commonly regarded as an intrinsic property of matter, but modern physics reveals particle masses to have complex origins, such as the Higgs mechanism in high-energy physics. In crystal lattices such as graphene, relativistic Dirac…

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). Using an algebraic classification of pseudo-Riemannian spaces in terms of the boost-weight…

It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…

We characterize the image of the Poisson transform on any distinguished boundary of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a generator system of a two sided…

Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to…

We present a criterion for deciding which compact extra dimensional spaces yield physically reliable Newton's law corrections. We study compact manifolds with boundary and without boundary. The boundary conditions which we use on the…

On the space of matrices with rational (trigonometric/elliptic) entries there is a well-known Lie-Poisson $r$-matrix structure. The known $r$-matrices are defined on the Riemann sphere (rational), the cylinder (trigonometric), or the torus…

The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…