Local quantum theory with braid group statistics

1993 ◽  
pp. 17-44
Author(s):  
Jürg Fröhlich ◽  
Thomas Kerler
Keyword(s):  
Quantum Theory ◽  
Braid Group ◽  
Local Quantum ◽  
Braid Group Statistics

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.

Quantum symmetry and braid group statistics inG-spin models

1993 ◽  
Vol 156 (1) ◽  
pp. 127-168 ◽  
Author(s):  
K. Szlachányi ◽  
P. Vecsernyés
Keyword(s):  
Braid Group ◽  
Spin Models ◽  
Quantum Symmetry ◽  
Braid Group Statistics

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.

SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE

1992 ◽  
Vol 04 (spec01) ◽  
pp. 113-157 ◽  
Author(s):  
KLAUS FREDENHAGEN ◽  
KARL-HENNING REHREN ◽  
BERT SCHROER
Keyword(s):  
Braid Group ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Cpt Symmetry ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Almost All ◽  
Conformal Covariance

The general theory of superselection sectors is shown to provide almost all the structure observed in two-dimensional conformal field theories. Its application to two-dimensional conformally covariant and three-dimensional Poincaré covariant theories yields a general spin-statistics connection previously encountered in more special situations. CPT symmetry can be shown also in the absence of local (anti-) commutation relations, if the braid group statistics is expressed in the form of an exchange algebra.

scholarly journals BRAID GROUP STATISTICS IN TWO-DIMENSIONAL QUANTUM FIELD THEORY

1996 ◽  
Vol 08 (07) ◽  
pp. 907-924 ◽  
Author(s):  
C. ADLER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Braid Group ◽  
Scattering Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Dimensional Minkowski Space ◽  
Braid Group Statistics

Within the framework of algebraic quantum field theory, we construct explicitly localized morphisms of a Haag-Kastler net in 1+1-dimensional Minkowski space showing abelian braid group statistics. Moreover, we investigate the scattering theory of the corresponding quantum fields.

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