Ebook: Noncommutative Differential Geometry and Its Applications to Physics: Proceedings of the Workshop at Shonan, Japan, June 1999

Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments.
However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium.
Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

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Content:
Front Matter....Pages i-viii
Methods of Equivariant Quantization....Pages 1-12
Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory....Pages 13-30
Geometrical Structures on Noncommutative Spaces....Pages 31-48
A Relation Between Commutative and Noncommutative Descriptions of D-Branes....Pages 49-61
Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0....Pages 63-98
D-Brane Actions on K?hler Manifolds....Pages 99-121
On The Projective Classification of the Modules of Differential Operators on ?m ....Pages 123-129
An Interpretation of the Schouten-Nijenhuis Bracket....Pages 131-143
Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators....Pages 145-154
C*-Algebraic Deformation and Index Theory....Pages 155-167
Singular Systems of Exponential Functions....Pages 169-186
Determinants of Elliptic Boundary Problems in Quantum Field Theory....Pages 187-215
On Geometry of Non-Abelian Duality....Pages 217-226
Weyl Calculus and Wigner Transform on the Poincar? Disk....Pages 227-243
Lectures on Graded Differential Algebras and Noncommutative Geometry....Pages 245-306
Back Matter....Pages 307-308

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Content:
Front Matter....Pages i-viii
Methods of Equivariant Quantization....Pages 1-12
Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory....Pages 13-30
Geometrical Structures on Noncommutative Spaces....Pages 31-48
A Relation Between Commutative and Noncommutative Descriptions of D-Branes....Pages 49-61
Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0....Pages 63-98
D-Brane Actions on K?hler Manifolds....Pages 99-121
On The Projective Classification of the Modules of Differential Operators on ?m ....Pages 123-129
An Interpretation of the Schouten-Nijenhuis Bracket....Pages 131-143
Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators....Pages 145-154
C*-Algebraic Deformation and Index Theory....Pages 155-167
Singular Systems of Exponential Functions....Pages 169-186
Determinants of Elliptic Boundary Problems in Quantum Field Theory....Pages 187-215
On Geometry of Non-Abelian Duality....Pages 217-226
Weyl Calculus and Wigner Transform on the Poincar? Disk....Pages 227-243
Lectures on Graded Differential Algebras and Noncommutative Geometry....Pages 245-306
Back Matter....Pages 307-308
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