Braid Statistics in Three-Dimensional Local Quantum Theory

1990 ◽  
pp. 15-79 ◽  
Author(s):  
J. Fröhlich ◽  
F. Gabbiani ◽  
P.-A. Marchetti
Keyword(s):  
Quantum Theory ◽  
Three Dimensional ◽  
Local Quantum

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.

Manifest non-locality in quantum mechanics, quantum field theory and quantum gravity

2019 ◽  
Vol 34 (28) ◽  
pp. 1941004
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Closed String ◽  
Covariant Formulation ◽  
Quantum Field ◽  
Quantum Geometry ◽  
Local Quantum ◽  
Generic Representation ◽  
Non Locality

We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

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.

scholarly journals A Three-Dimensional Non-Local Quantum Vacuum as the Origin of Photons

2020 ◽  
Vol 65 (2) ◽  
pp. 106
Author(s):  
D. Fiscaletti ◽  
A. Sorli
Keyword(s):  
Ground State ◽  
Three Dimensional ◽  
Black Body ◽  
Physical Reality ◽  
Density Fluctuations ◽  
Quantum Vacuum ◽  
Local Quantum ◽  
Non Local ◽  
Planck’S Law ◽  
Quantization Volume

A model of a three-dimensional quantum vacuum defined by the processes of creation/annihilation of quanta corresponding to elementary energy density fluctuations is proposed. In it, a photon is not a primary physical reality but emerges itself as a special state of the three-dimensional quantum vacuum. In this model, the three-dimensional quantum vacuum has a ground state which acts as a “cosmic reservoir” of photons, which emits and absorbs photons and Planck’s law of the spectral distribution of the energy radiated by a black body derives from the fundamental processes in the three-dimensional quantum vacuum, in particular, in the context of a quantization volume responsible for the appearance of photons. Finally, the idea of the Lamb shift of hydrogenoid atoms as a phenomenon determined by the ground state of the quantum vacuum which acts as a reservoir of photons is explored.

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