Advances in Applied Clifford Algebras

Proc. Suppl. 4, (S1), 1994

Proceedings of the XXIIth International Conference on
Differential Geometric Methods in Theoretical Physics

Contents:

1. Chapter 1: Quantum Groups, Hopf Algebras and Braided Geometry
2. Chapter 2: Noncommutative Differential Geometry
3. Chapter 3: Quantum Field Theory
4. Chapter 4: Classical Field Theory and Space-Time
5. Chapter 5: Clifford Algebras and Spinors
6. Chapter 6: Differential Equations and Geometry

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Organizer and Editors:

Zbigniew Oziewicz, Email: oziewicz@proton.ift.uni.wroc.pl
University of Wroclaw, Poland

International Advisory Committee:

Chapter 1: Quantum Groups, Hopf Algebras and Braided Geometry

• Page 3, Louis H. Kauffman, Ribbon Hopf algebras and invariants of 3-manifolds
• Page 21, Louis Crane, Louis H. Kauffman and David N. Yetter, On the classicality of Broda's SU(2) invariants of 4-manifolds
• Page 27, Louis Crane, Louis H. Kauffman and David N. Yetter, On the failure of the Lickorish encirclement. Lemma for Temperley-Lieb recoupling theory at certain roots of unity
• Page 33, Mico Durdevic, Quantum principal bundles
• Page 49, Thomas Kerler, On braided tensor categories
• Page 61, Shan Majid, Lie algebras and braided geometry
• Page 79, Cupatitzio Ramirez and Luis Urrutia, 3D Chern-Simons theories and their relation to quantum groups
• Page 87, Achim Kempf, On position and momentum operators in quantum mechanics with quantum group symmetry
• Page 95, Suemi Rodriguez-Romo, On SOq(3,1) q-Regularization

Chapter 2: Noncommutative Differential Geometry

• Page 105, Julius Wess, q-deformed quantization
• Page 113, Aristophanes Dimakis and Folkert Muller-Hoissen, Noncommutative differential calculus: quantum groups, stochastic processes and antibracket
• Page 125, Peter Schupp, Paul Watts and Bruno Zumino, Cartan calculus on quantum Lie algebras
• Page 135, Chryssomalis Chryssomalakos and Bruno Zumino, Integrals and Fourier transforms in quantum plane
• Page 145, Alexei P. Isaev, GLq(N)-covariant noncommutative geometry
• Page 157, Vladimir G. Pestov, On even collective effects in purely odd superspaces

Chapter 3: Quantum Field Theory

• Page 167, Alexander A. Voronov, Topological field theories, string backgrounds and homotopy algebras
• Page 179, Werner Nahm, Conformal field theory, dilogarithms, and 3-dimensional manifolds
• Page 193, Daniel Cangemi, 2-D gravities as gauge theories with extended groups
• Page 203, Klaus Lang and Werner Ruhl, Critical O(N)-vector nonlinear sigma models: resume of their field structure
• Page 217, Davide Franco and Cesare Reina, The geometry of quantum correction for topological sigma models: a simple example
• Page 223, Mark Temple-Raston, Solitons in topological field theories
• Page 229, Gerald V. Dunne, Classifcation of non-abelian Chern-Simons vortices
• Page 239, Louise Dolan, Free fermion constructions of super virasoro and super Kac-Moody algebras
• Page 247, Wolfgang Drechsler, Quantized de Sitter gauge theory with classical metric and axial torsion
• Page 259, Keiichi Akama and Ichiro Oda, BRST quantization of pregeometry and topological pregeometry
• Page 267, P. Fulan, Y.S. Stanev and I.T. Todorov, Exchange relations and corrrelation functions for an SO(4)-invariant quantum mechanical model
• Page 275, Jouko Mickelsson, Current algebra and renormalization

Chapter 4: Classical Field Theory and Space-Time

• Page 291, Leopold Halpern, Matter and Geometry in a Unified Theory
• Page 297, F. Delduc, L. Frappat, E. Ragoucy and Paul Sorba, General properties of classical W algebras
• Page 317, Thomas Gisiger and Manu B. Paranjape, Skyrmion-Skyrmion scattering
• Page 323, Michael Forger, New results on the canonical structure of classical non-linear sigma models
• Page 325, Magdalena Gusiew-Czudzak and Zbignew Oziewicz, Poincare-Cartan subbundles
• Page 341, Mauro Bregola and Carlo Ferrario, Hamilton's principle for constrained systems
• Page 349, Gerald Harnett, On the 2-cocycles of the Galilei lie algebra
• Page 357, Paolo Budinich, Conformal compactifications of space-time and momentum-space
• Page 367, Howard E. Brandt, Torsion relations in Finsler spacetime tangent bundle

Chapter 5: Clifford Algebras and Spinors

• Page 379, Jaime Keller, Clifford algebra and the construction of a theory of elementary particle fields
• Page 395, Frank Flaherty, Multiplication of spinors and the Dirac operator
• Page 405, Tatiana A. Ivanova and A.D. Popov, Solutions of the Yang-Mills equations and a Clifford algebras
• Page 413, Enrique Ramirez de Arellano, Michael V. Shapiro and Nikolai L. Vasilevski, Two types of analysis associated to the notion of Hurwitz pairs
• Page 423, Frank Sommen, Clifford tensor calculus
• Page 437, William M. Pezzaglia Jr. and Alfred W. Differ, A Clifford dyadic superfield from bilateral interactions of geometric multispin Dirac theory
• Page 447, Geoffrey Dixon, Division algebras, (1,9)-space-time, matter-antimatter mixing
• Page 455, Garret Sobczyk, Derivations of endomorphisms
• Page 461, Mico Durdevic and Zbigniew Oziewicz, Clifford Algebras and Spinors in Braided Geometry

Chapter 6: Differential Equations and Geometry

• Page 471, Vyacheslav Spiridonov, Luc Vinet and Alexei Zhedanov, Difference Schrodinger operators with the fixed symmetry properties
• Page 483, Allina A. Suzko, Supersymmetry and topological effects in quantum mechanical systems
• Page 491, M.A. Aguilar, J.M. Lopez-Romero and Miguel Socolovsky, Cohomology and Spectral sequences in gauge theory
• Page 501, Manlio Bordoni, A method to compare operators. Applications to Schrodinger and Dirac operators
• Page 509, Liudmila Sabinina, Trans-symmetric spaces
• Page 515, Geoffrey Martin, A geometric structure for the Lorentz-Dirac equation
• Page 531, Valery P. Karassiov, Polynomial Lie super algebras in composite models with internal symmetries

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