FLAT SUPERSYMMETRIC SPACE-TIME AND THE THEORY OF SUPER FIELDS

Flat supersymmetric space-time (x, θ) has been discussed under assumption that the Fermi variables are symplectic vectors only. We have abandoned the traditional assumption, that it must be the spinor representation of Lorentz group, which makes in the usual theory of supersymmetry.The even and odd generators of the ortho-symplectic group OS_p(414) have been calculated concretely in its dyads representation.New superfields, Lagrangian and the action integral, different from the usual theory, have been introduced in this flat case.

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.

On the Evolution of Approaches to the Space-Time Symmetry

The general space-time composition was analyzed starting in ancient times. During the previous three millenniums, to explain elementary physical phenomena, the world was twice admitted to be immersed into an “aether”. Presently the “aether” is assumed to be asymptotically close to the vacuum. This approximation is included in the foundation of the special theory of relativity.

Change of Space-Time Structure under Lorentz Transformation

When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will change the structure of the physical space-time and cause clock dilation effect. The study in this paper provides us with new insights to understand the essential and intrinsic relation between special relativity and general relativity. It provides us with a new way to unify special relativity and general relativity.

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

Geometrical Meaning of Time and the Theory of Relativity

New geometrical model of time is suggested where time of body’s motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to definite length of four-dimension trajectories that is clocks appear to be standards for measurements of length in four-dimension space analogously as hard sticks are standards for measurements of length in three-dimension space. This means that space and time are entities of the same geometrical nature. A suggested interpretation of time leads to necessity of changes in general theory of relativity. These changes are unessential for body’s motion in weak gravitational field.

Application of Scale Relativity (ScR) Theory to the Problem of a Particle in a Finite One-Dimensional Square Well (FODSW) Potential

In the present work, and along the lines of Hermann, ScR theory is applied to a finite one-dimensional square well potential problem. The aim is to show that scale relativity theory can reproduce quantum mechanical results without employing the Schr?dinger equation. Some mathematical difficulties that arise when obtaining the solution to this problem were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potential utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within limited local computer facilities [1,2]. Comparison of the present results with the corresponding results obtained from conventional quantum mechanics by solving the Schr?dinger equation, shows very good agreement. This agreement was improved further by optimizing the parameters used in the numerical simulations [1,3]. This represents a new example where scale relativity theory, based on a fractal space-time concept, can accurately reproduce quantum mechanical results without invoking the Schr?dinger equation.

Elements of Time

A clear mathematical theory of time remains one of the most difficult challenges of science, which seems highly intriguing. In this work, we assume that time is the main independent attribute of nature and therefore may serve as the foundation of a comprehensive field theory. Furthermore, we assume that division algebras with the Euclidean norm are essential mathematical tools of time and the physical world in general. We use a four-dimensional normed division algebra of quaternions to describe time mathematically, as originally envisioned by Hamilton. We systematically define basic quaternion concepts related to time, such as the quaternion time interval, scalar measured time, the arrow of time, vector velocity, and quaternion frequency. We apply quaternion time concepts to the optical Doppler effect and demonstrate that our approach predicts known experimental results. Furthermore, we show that the quaternion solution of the Doppler effect enhances the relativity theory by resolving the notorious twin paradox. We identify quaternion frequency with the traditional concept of energy. We assume that quaternion energy, which is generally dependent on time and external interactions, can be used to describe dynamic properties of matter. In conclusion, we suggest that a state of matter can be represented by the eight-dimensional octonion configuration space, consisting of a quaternion time interval and a time dependent quaternion frequency. Therefore, it appears that the application of normed division algebras for the study of time and nature is highly logical, credible, and compelling.

Theory and practice of runoff space-time distribution

Based on the domestic and foreign concerning researches, this paper submits the runoff space-time distribution theory which shows evident scientific significances and powerful practical functions. On the basis of digital basin unit cell deriving from the digital elevation model (DEM) and assumption of linear confluence, this theory has been applied successfully to the runoff correlation researches in humid regions. In order to prove the adaptability of the theory in arid and semi-drought regions, this paper is used to the runoff correlation analysis in Wuding River basin——a tributary of Yellow River Basin, and has gained preliminary effective verification.

The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

In this short survey, we give a complete list of the most important results obtained by El Naschie’s E-infinity Cantorian space-time theory in the realm of quantum physics and cosmology. Special attention is paid to his recent result on dark energy and revising Einstein’s famous formula .

Ultrafast multi-target control of tightly focused light fields

The control of ultrafast optical field is of great interest in developing ultrafast optics as well as the investigation on vari-ous light-matter interactions with ultrashort pulses.However,conventional spatial encoding approaches have only lim-ited steerable targets usually neglecting the temporal effect,thus hindering their broad applications.Here we present a new concept for realizing ultrafast modulation of multi-target focal fields based on the facile combination of time-depend-ent vectorial diffraction theory with fast Fourier transform.This is achieved by focusing femtosecond pulsed light carrying vectorial-vortex by a single objective lens under tight focusing condition.It is uncovered that the ultrafast temporal de-gree of freedom within a configurable temporal duration(~400 fs)plays a pivotal role in determining the rich and exotic features of the focused optical field at one time,namely,bright-dark alternation,periodic rotation,and longitudinal/trans-verse polarization conversion.The underlying control mechanisms have been unveiled.Besides being of academic in-terest in diverse ultrafast spectral regimes,these peculiar behaviors of the space-time evolutionary beams may underpin prolific ultrafast-related applications such as multifunctional integrated optical chip,high-efficiency laser trapping,micro-structure rotation,super-resolution optical microscopy,precise optical measurement,and liveness tracking.

Modeling of Data Reduction in Wireless Sensor Networks

In this paper, we present a stochastic model for data in a Wireless Sensor Network (WSN) using random field theory. The model captures the space-time behavior of the underlying phenomenon being observed by the network. We present results regarding the size and spatial distribution of the regions of the network that sense statistically extreme values of the underlying phenomenon using the theory of extreme excursion regions. These results compliment many existing works in the literature that describe algorithms to reduce the data load, but lack an analytical approach to evaluate the size and spatial distribution of this load. We show that if only the statistically extreme data is transmitted in the network, then the data load can be significantly reduced. Finally, a simple performance model of a WSN is developed based on a collection of asynchronous M/M/1 servers that work in parallel. We derive several performance measures from this performance model. The presented results will be useful in the design of large scale sensor networks.

A Tentative Analysis of the Relationship between Thought and Language

Being a classical theory in the field of linguistics, the relationship between thought and language has been drawing the attentions of linguists, psychologists, sociologists and anthropologists to carry out a great deal of researches and debates. Sapir-Whorf Hypothesis about the relationship between thought and language is both influential and controversial .

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.

The Solution Cosmological Constant Problem

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by the Quantum Field Theory is about 120 orders of magnitude larger then the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff-Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that the Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way. We argue that there exists hidden physical mechanism which cancels divergences in canonical QED4, QCD4, Higher-Derivative-Quantum gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost fields really exist. It means that there exists the ghost-driven acceleration of the universe hidden in cosmological constant. In order to obtain the desired physical result we apply the canonical Pauli-Villars regularization up to Λ*. This would fit in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below the scale Λ*, i.e., The small value of the cosmological constant is explained by tiny violation of the symmetry between standard matter and ghost matter. Dark matter nature is also explained using a common origin of the dark energy and dark matter phenomena.

Unification Might Be Achievable by a Hypothesis of Instantaneous Time-Jumps during Photon and Graviton Interactions (A Brief Note)

Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.