scholarly journals Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems

1994 ◽  
Vol 85 (3) ◽  
pp. 483-496 ◽  
Author(s):  
D. Jacak ◽  
L. Jacak ◽  
K. Wieczorek
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Particle Systems ◽  
Mathematical Methods

scholarly journals LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS

1996 ◽  
Vol 11 (11) ◽  
pp. 899-913 ◽  
Author(s):  
N. FLEURY ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Equation Of Motion ◽  
Coset Space ◽  
One Dimensional ◽  
The One

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

An application of braid group theory to the finite time dead-core rate

2010 ◽  
Vol 10 (4) ◽  
pp. 835-855 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Hiroshi Matano ◽  
Chin-Chin Wu
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Finite Time ◽  
Dead Core

Rotations of 4nπ Research and no Twisted Mechanism Example Analysis Based on the Theory of Braid Group

2014 ◽  
Vol 536-537 ◽  
pp. 1355-1360
Author(s):  
Zhi Yu Fu ◽  
Lu Bin Hang ◽  
Hai Xu ◽  
Jin Cai ◽  
Huai Qiang Bian ◽  
...  
Keyword(s):  
Group Theory ◽  
Mechanism Design ◽  
Braid Group ◽  
Twisted State ◽  
Braid Theory

The Cable or Pipe between the Two Relatively Rotating Platforms Exists the Twisted Problem. from Viewpoint of Braid Group Theory, Rope’s Twisted State is Researched on. Based on the Characteristics of a Special Garside Braids Δn and Δnk , the Equivalence of Two Rotation Modes is Revealed. also, that the Determination of Rotation Mode’s Minimum Rotate Range is 4∏ while Using Braid Theory is Proposed. the Theory of Braid Group can Not only be Used as a Criterion for Determine Whether the Cable is Twisted, Finally, but also can be Used as Avoid Cable Twisted during Mechanism Design.

FINITE LINEAR QUOTIENTS OF ${\mathcal{B}}_3$ OF LOW DIMENSION

2010 ◽  
Vol 19 (05) ◽  
pp. 587-600 ◽  
Author(s):  
ERIC C. ROWELL ◽  
IMRE TUBA
Keyword(s):  
Group Theory ◽  
Irreducible Representation ◽  
Quantum Groups ◽  
Braid Group ◽  
Computational Group Theory ◽  
Finite Image ◽  
Low Dimension ◽  
Finite Linear ◽  
Linear Quotients

We study the problem of deciding whether or not the image of an irreducible representation of the braid group [Formula: see text] of degree ≤ 5 has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm that determines when the images are finite or infinite in all but finitely many cases, and use these results to study examples coming from quantum groups. Our technique uses two classification theorems and the computational group theory package GAP.

Composite Fermions in Braid Group Terms

2010 ◽  
Vol 17 (01) ◽  
pp. 53-71
Author(s):  
J. Jacak ◽  
I. Jóźwiak ◽  
L. Jacak
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Charged Particle ◽  
Braid Group ◽  
Quantum Information Processing ◽  
Particle Systems ◽  
Unitary Representations ◽  
Composite Fermions ◽  
Cyclotron Motion ◽  
One Dimensional

A new implementation of composite fermions, and more generally — of composite anyons is formulated, exploiting one-dimensional unitary representations of appropriately constructed subgroups of the full braid group, in accordance with a cyclotron motion of 2D charged particle systems. The nature of hypothetical fluxes attached to the Jain's composite fermions is explained via additional cyclotron trajectory loops consistently with braid subgroup structure. It is demonstrated that composite fermions and composite anyons are rightful 2D particles (not an auxiliary construction) associated with cyclotron braid subgroups instead of the full braid group, which may open a new opportunity for non-Abelian composite anyons for quantum information processing applications.

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