scholarly journals On the geometry of the space-time and motion of the spinning bodies

Open Physics ◽  
2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Kostadin Trenčevski
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Alternative Theory ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Classical Formulation ◽  
Time And Motion ◽  
Spinning Bodies ◽  
Spatial Rotations ◽  
The Universe

AbstractIn this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3 × 3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space S × SR, which appears to be isomorphic to SO(3,ℝ) × SO(3,ℝ) or S 3 × S 3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton’s third law in its classical formulation. The precession of the spinning axis is also considered.

A Note on the Representation of Clifford Algebras

2021 ◽  
Vol 62 ◽  
pp. 29-52
Author(s):  
Ying-Qiu Gu ◽  
Keyword(s):  
Clifford Algebras ◽  
Dimensional Space ◽  
Number System ◽  
Space Time ◽  
Coordinate Frame ◽  
Practical Calculation ◽  
3 Dimensional ◽  
Covariant Derivatives ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $\mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.

scholarly journals Summary Talk : Multi-Wavelength Sky Surveys

1998 ◽  
Vol 179 ◽  
pp. 493-499
Author(s):  
O. Lahav
Keyword(s):  
Gamma Rays ◽  
Dimensional Space ◽  
Instrument Design ◽  
List Type ◽  
Type Number ◽  
Sky Surveys ◽  
3 Dimensional ◽  
Multi Wavelength ◽  
The Universe ◽  
Summary Talk

An astronomer's career can be viewed in a 3-dimensional space where the (nearly orthogonal) axes are : – the objects of interest (from planets to the Universe),– techniques (from instrument design to analytic calculations),– the wavelength (from the radio to gamma rays).

Spin-one Duffin–Kemmer–Petiau equation in the presence of Manning–Rosen potential plus a ring-shaped-like potential

2014 ◽  
Vol 92 (6) ◽  
pp. 465-471 ◽  
Author(s):  
H. Hassanabadi ◽  
M. Kamali ◽  
B.H. Yazarloo
Keyword(s):  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Numerical Results ◽  
Centrifugal Term ◽  
Exponential Approximation ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
Rosen Potential ◽  
Uvarov Method

We present the solution of the Duffin–Kemmer–Petiau equation for Manning–Rosen potential plus a ring-shaped-like potential in (1+3)-dimensional space–time for spin-one particles within the framework of an exponential approximation for the centrifugal term. We have used the Nikiforov–Uvarov method in our calculations. The radial wavefunction and the angular wavefunctions are expressed in terms of Jacobi polynomials. We have also represented some numerical results for the Manning–Rosen potential plus a ring-shaped-like potential.

Volume (3-dimensional) space-time reconstruction of esophageal peristaltic contraction by using simultaneous US and manometry

2003 ◽  
Vol 58 (6) ◽  
pp. 913-919 ◽  
Author(s):  
Qing Dai ◽  
Ji-Bin Liu ◽  
James G Brasseur ◽  
Vinod K Thangada ◽  
Beje Thomas ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
3 Dimensional ◽  
Peristaltic Contraction ◽  
Dimensional Space Time

scholarly journals The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
J. A. Helayël-Neto ◽  
Alireza Sepehri ◽  
Tooraj Ghaffary
Keyword(s):  
Modified Gravity ◽  
Dimensional Space ◽  
Main Idea ◽  
Big Bang ◽  
Space Time ◽  
Dimensional Manifold ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
The Big Bang ◽  
Chern Simons

It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

scholarly journals THE WARPING OF EXTRA SPACES ACCELERATES THE EXPANSION OF THE UNIVERSE

2010 ◽  
Vol 19 (14) ◽  
pp. 2281-2287 ◽  
Author(s):  
ISHWAREE P. NEUPANE
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
De Sitter ◽  
Four Dimensions ◽  
Accelerating Expansion ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Expansion Of The Universe ◽  
Theories Of Gravity ◽  
The Universe

Generic cosmological models derived from higher-dimensional theories with warped extra-dimensions have a nonzero cosmological constant-like term induced on the 3 + 1 space–time, or a physical three-brane. In the scenario where this 3 + 1 space–time is an inflating de Sitter "bran" embedded in a higher-dimensional space–time, described by warped geometry, the four-dimensional cosmological term is determined in terms of two length scales: one is a scale associated with the size of extra-dimension(s) and the other is a scale associated with the warping of extra-space(s). The existence of this term in four dimensions provides a tantalizing possibility of explaining the observed accelerating expansion of the universe from fundamental theories of gravity, e.g. string theory.

Compton Wavelengths for the Proton and Electron May Differ by Hyperspace Geometry: Are they the same Particle Bifurcated?

2015 ◽  
Vol 61 ◽  
pp. 101-104
Author(s):  
Michael A. Persinger ◽  
Linda S. St-Pierre
Keyword(s):  
Gravitational Constant ◽  
Dimensional Space ◽  
Neutral Hydrogen ◽  
Space Time ◽  
Shared Variable ◽  
Dimensional Space Time ◽  
Order Of Magnitude ◽  
The Difference ◽  
Geometric Constant ◽  
The Universe

The discrepancy between the Compton wavelength of a proton and an electron has been assumed to reflect some shared variable with their respective masses. However this discrepancy of 1.83·103 is remarkably similar to the geometric constant (21.3 π4) derived from the product of four dimensional space-time for closed circular boundaries. This same formulation, when the appropriate powers for Newton’s Gravitational Constant and the mass, duration, and length of the universe were multiplied, resulted in a diffusivity value that has been considered a potential entanglement velocity. This value is the same order of magnitude as the ratio of 2π multiplied by the neutral hydrogen wavelength divided by a quantum “jiffy”. The quantifications suggest that the difference between the space, as inferred by wavelength, occupied by the electron and the proton are related by the geometric structure of space-time. Their distinctions as different particles are manifested when the temporal increments of observations are much, much less than the duration of the universe.

scholarly journals Irreducibility of some unitary representations of the poincaré group with respect to the Poincaré subsemigroup, II

1982 ◽  
Vol 87 ◽  
pp. 147-174 ◽  
Author(s):  
Hitoshi Kaneta
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Unitary Representations ◽  
Poincaré Group ◽  
Poincare Group ◽  
3 Dimensional ◽  
The Matrix ◽  
Dimensional Space Time

Let P+(3) and P+(3) be the 3-dimensional space-time Poincaré group and the Poincaré subsemigroup, that is, P(3) = R3 × sSU(1, 1) and P+(3) = V+(3)=SSU(1, 1) where The multiplication is defined by the formula (x, g)(x′, g′) = (x + g*−1x′g−1, gg′) for x, x′ ∈ R3 and g, g′ ∈ SU(l, 1). Here x = (x0, x1, x2) is identified with the matrix

Extrema in Space-Time

1966 ◽  
Vol 18 ◽  
pp. 678-691 ◽  
Author(s):  
Louis V. Quintas ◽  
Fred Supnick
Keyword(s):  
Fundamental Form ◽  
Radio Signal ◽  
Dimensional Space ◽  
Space Time ◽  
Finite Set ◽  
Dimensional Space Time ◽  
History Of ◽  
Image Position ◽  
The Universe

Consider an astronomer and his observation field, i. e., the set of observable (light or radio) signal-emitting loci of the universe. Let the observation field be ordered by attaching a date to each observable locus indicating the time in the history of the universe that the signal was emitted from its source. Whereas both the astronomer and his observation field age with time, the observations of the astronomer may trace a sequence of loci whose time labels proceed forward or backward in time (cf. Appendix).Consider now a finite set S of events in Ln,n-dimensional space-time (Riemannian n-space having the fundamental form

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