Coverart for item
The Resource Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]

Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]

Label
Quantum groups, quantum categories, and quantum field theory
Title
Quantum groups, quantum categories, and quantum field theory
Statement of responsibility
Jürg Fröhlich, [Thomas Kerler]
Creator
Contributor
Subject
Language
eng
Summary
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students
Member of
Action
digitized
Cataloging source
SPLNM
http://library.link/vocab/creatorName
Fröhlich, Jürg
Dewey number
530.1/43
Illustrations
illustrations
Index
index present
LC call number
  • QC20.7.G76
  • QA3
LC item number
  • F76 1993
  • .L28 no. 1542
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1965-
http://library.link/vocab/relatedWorkOrContributorName
Kerler, Thomas
Series statement
Lecture notes in mathematics,
Series volume
1542
http://library.link/vocab/subjectName
  • Quantum groups
  • Quantum field theory
  • Quantum field theory
  • Quantum groups
  • Kwantumveldentheorie
  • Quantengruppe
  • Quantenfeldtheorie
  • Kategorientheorie
Label
Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 422-428) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Introduction and Survey of Results -- 2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of Low-Dimensional, Local Quantum Field Theory. 2.2. Generalities Concerning Algebraic Field Theory. 2.3. Statistics and Fusion of Intertwiners; Statistical Dimensions. 2.4. Unitary Representations of the Braid Groups Derived from Local Quantum Theory; Markov Traces -- 3. Superselection Sectors and the Structure of Fusion Rule Algebras. 3.1. Definition of and General Relations in Fusion Rule Algebras and their Appearance in Local Quantum Field Theories. 3.2. Structure Theory for Fusion Rule Algebras. 3.3. Grading Reduction with Automorphisms and Normality Constraints in Fusion Rule Algebras. 3.4. Fusionrules with a Generator of Dimension not Greater than Two -- 4. Hopf Algebras and Quantum Groups at Roots of Unity -- 5. Representation Theory of [actual symbol not reproducible]. 5.1. Highest Weight Representations of [actual symbol not reproducible]
  • 5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and q-Dimensions: Selecting a List of Physical Representations -- 6. Path Representations of the Braid Groups for Quantum Groups at Roots of Unity. 6.1. Quotients of Representation Categories. 6.2. Braid Group Representations and Fusion Equations. 6.3. Unitarity of Braid Group Representations Obtained from U[subscript q](sl[subscript d + 1]). 6.4. Markov Traces -- 7. Duality Theory for Local Quantum Theories, Dimensions and Balancing in Quantum Categories. 7.1. General Definitions, Towers of Algebras. 7.2. Quantum Group Symmetries of Charged Fields. 7.3. The Index and Fundamental Decompositions. 7.4. Balancing Phases. 7.5. Theta -- Categories -- 8. The Quantum Categories with a Generator of Dimension less than Two. 8.1. Product Categories and Induced Categories. 8.2. The A[subscript n] -- Categories and Main Results
  • A: Undirected Graphs with Norm not Larger than Two. A.1. Bicolorable, finite graphs. A.2. Bicolorable, infinite graphs (corresponding to N = [actual symbol not reproducible]). A.3. Non-bicolorable, finite graphs. A.4. Non-bicolorable, infinite graphs (N = [actual symbol not reproducible]). A.5. The higher graded fusionrule algebras -- B: Fusion Rule Algebra Homomorphisms. B.1. [actual symbol not reproducible]. B.2. [actual symbol not reproducible]. B.3. [actual symbol not reproducible]. B.4. [actual symbol not reproducible] -- Bibliography -- Index
Control code
298692436
Dimensions
unknown
Extent
1 online resource (vii, 431 pages)
Form of item
online
Isbn
9783540476115
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)298692436
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Label
Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
Publication
Bibliography note
Includes bibliographical references (pages 422-428) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Introduction and Survey of Results -- 2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of Low-Dimensional, Local Quantum Field Theory. 2.2. Generalities Concerning Algebraic Field Theory. 2.3. Statistics and Fusion of Intertwiners; Statistical Dimensions. 2.4. Unitary Representations of the Braid Groups Derived from Local Quantum Theory; Markov Traces -- 3. Superselection Sectors and the Structure of Fusion Rule Algebras. 3.1. Definition of and General Relations in Fusion Rule Algebras and their Appearance in Local Quantum Field Theories. 3.2. Structure Theory for Fusion Rule Algebras. 3.3. Grading Reduction with Automorphisms and Normality Constraints in Fusion Rule Algebras. 3.4. Fusionrules with a Generator of Dimension not Greater than Two -- 4. Hopf Algebras and Quantum Groups at Roots of Unity -- 5. Representation Theory of [actual symbol not reproducible]. 5.1. Highest Weight Representations of [actual symbol not reproducible]
  • 5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and q-Dimensions: Selecting a List of Physical Representations -- 6. Path Representations of the Braid Groups for Quantum Groups at Roots of Unity. 6.1. Quotients of Representation Categories. 6.2. Braid Group Representations and Fusion Equations. 6.3. Unitarity of Braid Group Representations Obtained from U[subscript q](sl[subscript d + 1]). 6.4. Markov Traces -- 7. Duality Theory for Local Quantum Theories, Dimensions and Balancing in Quantum Categories. 7.1. General Definitions, Towers of Algebras. 7.2. Quantum Group Symmetries of Charged Fields. 7.3. The Index and Fundamental Decompositions. 7.4. Balancing Phases. 7.5. Theta -- Categories -- 8. The Quantum Categories with a Generator of Dimension less than Two. 8.1. Product Categories and Induced Categories. 8.2. The A[subscript n] -- Categories and Main Results
  • A: Undirected Graphs with Norm not Larger than Two. A.1. Bicolorable, finite graphs. A.2. Bicolorable, infinite graphs (corresponding to N = [actual symbol not reproducible]). A.3. Non-bicolorable, finite graphs. A.4. Non-bicolorable, infinite graphs (N = [actual symbol not reproducible]). A.5. The higher graded fusionrule algebras -- B: Fusion Rule Algebra Homomorphisms. B.1. [actual symbol not reproducible]. B.2. [actual symbol not reproducible]. B.3. [actual symbol not reproducible]. B.4. [actual symbol not reproducible] -- Bibliography -- Index
Control code
298692436
Dimensions
unknown
Extent
1 online resource (vii, 431 pages)
Form of item
online
Isbn
9783540476115
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)298692436
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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