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.

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 Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

4 + n -dimensional Topoisomerase-like Waves

2018 ◽  
Author(s):  
Alireza Sepehri
Keyword(s):  
Extra Dimensions ◽  
Dimensional Space ◽  
Space Time ◽  
Dimensional Manifold ◽  
Curved Space ◽  
New Model ◽  
Exchange Information ◽  
Dimensional Space Time ◽  
Dimensional Object

In this paper, we propose a new model which allows to consider all evolutions of DNA from viewpoint of an observer on 11-dimensional manifold. In this model, DNA is an 4 + n-dimensional object in 11 dimensional space-time which is compacted to 4-dimensional manifold. This leads to the emergence of a curved space-time around DNA and production of some new waves. To exchange information between DNAs, it is needed that waves play the role of topoisomerases in extra dimensions. These topoisomerase-like waves open packings of DNA, read it’s information and compact it again. The shape and properties of these waves are completely different from gravitational and electromagnetic ones. By reducing dimensions from 11 to 4, the topoisomerase-like waves obtain the properties of known fields like gravitons and photons.

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 Higher Dimensional Bianchi Type-III String Cosmological Models in Lyra Geometry

2021 ◽  
Author(s):  
Kangujam Priyokumar Singh ◽  
Jiten Baro ◽  
Asem Jotin Meitei ◽  
S. Romaleima Devi
Keyword(s):  
Bianchi Type ◽  
Dimensional Space ◽  
Big Bang ◽  
Lyra Geometry ◽  
Space Time ◽  
Cosmological Models ◽  
Model Universe ◽  
Type Iii ◽  
First Case ◽  
Dimensional Space Time

Here we studied Bianchi type-III string cosmological models generated by means of a cloud of strings with particles connected to them in the framework of Lyra geometry considering five-dimensional space-time. To obtain the exact solutions of field equations we consider that the shear scalar and the scalar expansion are proportional, σ∞θ which leads to D=cn and secondly we adopt the assumption considering the Reddy String Condition, ρ+λ=0. From the two different cases obtained here, first case leads to the Bianchi type-III string cosmological model in Lyra geometry in five-dimensional space-time and the second case leads to the five-dimensional vacuum universe in general relativity. The Geometrical and physical properties of the model universe are studied comparing with the present day’s observational findings. The model universe obtained here starts with the big bang and as time progresses both particle density ρp and energy density ρ decreases with expansion of our Universe.

4 + n -dimensional Topoisomerase-like Waves

2018 ◽  
Author(s):  
Alireza Sepehri
Keyword(s):  
Extra Dimensions ◽  
Dimensional Space ◽  
Space Time ◽  
Dimensional Manifold ◽  
Curved Space ◽  
New Model ◽  
Exchange Information ◽  
Dimensional Space Time ◽  
Dimensional Object

In this paper, we propose a new model which allows to consider all evolutions of DNA from viewpoint of an observer on 11-dimensional manifold. In this model, DNA is an 4 + n-dimensional object in 11 dimensional space-time which is compacted to 4-dimensional manifold. This leads to the emergence of a curved space-time around DNA and production of some new waves. To exchange information between DNAs, it is needed that waves play the role of topoisomerases in extra dimensions. These topoisomerase-like waves open packings of DNA, read it’s information and compact it again. The shape and properties of these waves are completely different from gravitational and electromagnetic ones. By reducing dimensions from 11 to 4, the topoisomerase-like waves obtain the properties of known fields like gravitons and photons.

4 + n -dimensional Topoisomerase-like Waves

2018 ◽  
Author(s):  
Alireza Sepehri
Keyword(s):  
Extra Dimensions ◽  
Dimensional Space ◽  
Space Time ◽  
Dimensional Manifold ◽  
Curved Space ◽  
New Model ◽  
Exchange Information ◽  
Dimensional Space Time ◽  
Dimensional Object

In this paper, we propose a new model which allows to consider all evolutions of DNA from viewpoint of an observer on 11-dimensional manifold. In this model, DNA is an 4 + n-dimensional object in 11 dimensional space-time which is compacted to 4-dimensional manifold. This leads to the emergence of a curved space-time around DNA and production of some new waves. To exchange information between DNAs, it is needed that waves play the role of topoisomerases in extra dimensions. These topoisomerase-like waves open packings of DNA, read it’s information and compact it again. The shape and properties of these waves are completely different from gravitational and electromagnetic ones. By reducing dimensions from 11 to 4, the topoisomerase-like waves obtain the properties of known fields like gravitons and photons.

THE CHERN–SIMONS TERM AND THE DYNAMICS OF THE CPn−1 MODEL IN THREE DIMENSIONS

1992 ◽  
Vol 07 (03) ◽  
pp. 619-630 ◽  
Author(s):  
E. ABDALLA ◽  
F. M. DE CARVALHO
Keyword(s):  
Phase Structure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Three Dimensions ◽  
Rich Phase ◽  
Large N ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space

We analyze the phase structure of the CPn−1 model in three-dimensional space–time coupled to fermions, paying special attention to the role played by the Chern–Simons term generated by the fermions. A rich phase structure arises from the large-n expansion.

IS THERE A STATISTICS TRANSMUTATION DUE TO INTERACTION WITH THE CHERN-SIMONS FIELD?

1991 ◽  
Vol 06 (08) ◽  
pp. 1313-1318 ◽  
Author(s):  
G.G. NANOBASHVILI ◽  
G.P. PRON’KO
Keyword(s):  
Dimensional Space ◽  
Geometric Quantization ◽  
Classical Mechanics ◽  
Scalar Particle ◽  
Space Time ◽  
Apparent Contradiction ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Particle Statistics

The classical mechanics of a scalar particle interacting with a Chern-Simons field in the (2+1)-dimensional space-time has been considered. The geometric quantization of this system does not lead to particle statistics transmutation. This result is in apparent contradiction with the statement of Ref. 1.

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