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.

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.

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.

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.

INDUCED PARITY VIOLATION ANOMALY FOR THE PROCA FIELD IN A THREE-DIMENSIONAL SPACE–TIME

1999 ◽  
Vol 14 (02) ◽  
pp. 271-280
Author(s):  
E. R. BEZERRA DE MELLO ◽  
V. M. MOSTEPANENKO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Space Time ◽  
Simons Theory ◽  
Proca Field ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space ◽  
Chern Simons Theory

In this paper we develop diagrammatic computations of spontaneous parity-violating anomalies for a complex massive vector field (Proca field) induced by its interaction with an electromagnetic field in a three-dimensional space–time. We also calculate the effective potential energy between two charged particles in Maxwell–Chern–Simons theory in a nonrelativistic limit.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Electromagnetic Casimir effect of concentric cylinders in (D + 1)-dimensional space–time

2019 ◽  
Vol 34 (08) ◽  
pp. 1950035
Author(s):  
Chun Yong Chew ◽  
Yong Kheng Goh
Keyword(s):  
Boundary Condition ◽  
Interaction Energy ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Order Term ◽  
Perturbation Technique ◽  
Space Time ◽  
Concentric Cylinders ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

We study the electromagnetic Casimir interaction energy between two parallel concentric cylinders in [Formula: see text]-dimensional Minkowski space–time for different combinations of perfectly conducting boundary condition and infinitely permeable boundary condition. We consider two cases where one cylinder is outside each other and where one is inside the other. By solving the equation of motion and computing the TGTG formulas, explicit formulas for the Casimir interaction energy can be derived and asymptotic behavior of the Casimir interaction energy in the nanoregime is calculated by using perturbation technique. We computed the interaction energy analytically up to next-to-leading order term.

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