相关论文: Yank and Hooke's constant group theoretically
The current article continues our project on representation theory, Euler elements, causal homogeneous spaces and Algebraic Quantum Field Theory (AQFT). We call a pair (h,k) of Euler elements orthogonal if $e^{\pi i \ad h} k = -k$. We show…
Possibly, the most general action in the background of isotropic and homogeneous space-time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective…
Taking into account four universal constants, namely the Planck's constant $h$, the velocity of light $c$, the constant of gravitation $G$ and the Boltzmann's constant $k$ leads to structuring theoretical physics in terms of three theories…
There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that…
We compare two ways of force terms generating in the model of nonrelativistic particle moving in the presence of constant field force $\vec{F}$. First of them uses the twist-deformed acceleration-enlarged Newton-Hooke quantum space-times…
In this paper we generalize some of these results for loop algebras and groups as well as for the Virasoro algebra to the two-dimensional case. We define and study a class of infinite dimensional complex Lie groups which are central…
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal…
We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orthogonal, unitary and symplectic groups of adjacent dimensions…
We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem,…
We investigate the adiabatic orbital evolution of a point particle in the Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is enough smaller than the typical timescale of…
By means of a general classification of the different kinds of matter of nature form a chain from the world of the subatomic particles to the large bodies of the universe, the galaxies. Then, it proposes a new baryonic force for the…
The general class of the graded Lie algebras is defined. These algebras could be constructed using an arbitrary dynamical systems with discrete time and with invarinat measure. In this papers we consider the case of the central extension of…
Classical mechanical systems are defined by their kinetic and potential energies. They generate a Lie algebra under the canonical Poisson bracket. This Lie algebra, which is usually infinite dimensional, is useful in analyzing the system,…
We briefly indicate some implications of [1] for the second Lie algebra cohomology of equivariant map algebras and (twisted multi) loop algebras.
In classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory…
Let $(V,\gamma )$ be a real finite dimensional vector space with a symmetric bilinear form $\gamma $ whose kernel is spanned by a nonzero vector. The set of invertible real linear mappings of $(V, \gamma )$ into itself forms a Lie group…
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue…
In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortun\'e & Vall\'ee. Linear isotropic constitutive relations for stress and hyperstress in…
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry.…
We study observation entropy (OE) for the Quantum kicked top (QKT) model, whose classical counterpart possesses different phases: regular, mixed, or chaotic, depending on the strength of the kicking parameter. We show that OE grows…