Three-dimensional analytical infinite order sudden quantum theory for triatomic indirect photodissociation processes

1997 ◽  
Vol 107 (6) ◽  
pp. 1835-1848
Author(s):  
Horacio Grinberg ◽  
Karl F. Freed ◽  
Carl J. Williams
Keyword(s):  
Quantum Theory ◽  
Infinite Order ◽  
Three Dimensional

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

BRAID STATISTICS IN LOCAL QUANTUM THEORY

1990 ◽  
Vol 02 (03) ◽  
pp. 251-353 ◽  
Author(s):  
J. FRÖHLICH ◽  
F. GABBIANI
Keyword(s):  
Quantum Theory ◽  
Conformal Symmetry ◽  
Three Dimensional ◽  
Space Time ◽  
Braid Groups ◽  
Classification Theory ◽  
Mapping Class ◽  
Systematic Classification ◽  
Algebraic Quantum ◽  
Local Quantum

We present details of a mathematical theory of superselection sectors and their statistics in local quantum theory over (two- and) three-dimensional space-time. The framework for our analysis is algebraic quantum field theory. Statistics of superselection sectors in three-dimensional local quantum theory with charges not localizable in bounded space-time regions and in two-dimensional chiral theories is described in terms of unitary representations of the braid groups generated by certain Yang-Baxter matrices. We describe the beginnings of a systematic classification of those representations. Our analysis makes contact with the classification theory of subfactors initiated by Jones. We prove a general theorem on the connection between spin and statistics in theories with braid statistics. We also show that every theory with braid statistics gives rise to a “Verlinde algebra”. It determines a projective representation of SL(2, ℤ) and, presumably, of the mapping class group of any Riemann surface, even if the theory does not display conformal symmetry.

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