LECTURES ON ADVANCED MATHEMATICAL METHODS FOR PHYSICISTS

LECTURES ON ADVANCED MATHEMATICAL METHODS FOR PHYSICISTS

CONTENTS


FRONT MATTER Sunil Mukhi and N. Mukunda	i
Part I: Topology and Differential Geometry
Topology and Differential Geometry — Introduction to Part I Sunil Mukhi	1
Topology Sunil Mukhi and N. Mukunda	5
Homotopy Sunil Mukhi and N. Mukunda	21
Differentiable Manifolds I Sunil Mukhi and N. Mukunda	41
Differentiable Manifolds II Sunil Mukhi and N. Mukunda	65
Homology and Cohomology Sunil Mukhi and N. Mukunda	87
Fibre Bundles Sunil Mukhi and N. Mukunda	105
Bibliography for Part I Sunil Mukhi and N. Mukunda	117
Part II: Group Theory and Structure and Representations of Compact Simple Lie Groups and Algebras
Group Theory and Structure and Representations of Compact Simple Lie Groups and Algebras — Introduction to Part II N. Mukunda	119
Review of Groups and Related Structures Sunil Mukhi and N. Mukunda	123
Review of Group Representations Sunil Mukhi and N. Mukunda	135
Lie Groups and Lie Algebras Sunil Mukhi and N. Mukunda	147
Linear Representations of Lie Algebras Sunil Mukhi and N. Mukunda	165
Complexification and Classification of Lie Algebras Sunil Mukhi and N. Mukunda	171
Geometry of Roots for Compact Simple Lie Algebras Sunil Mukhi and N. Mukunda	183
Positive Roots, Simple Roots, Dynkin Diagrams Sunil Mukhi and N. Mukunda	189
Lie Algebras and Dynkin Diagrams for SO(2l), SO(2l + 1), USp(2l), SU(l + 1) Sunil Mukhi and N. Mukunda	197
Complete Classification of All CSLA Simple Root Systems Sunil Mukhi and N. Mukunda	215
Representations of Compact Simple Lie Algebras Sunil Mukhi and N. Mukunda	227
Spinor Representations for Real Orthogonal Groups Sunil Mukhi and N. Mukunda	245
Spinor Representations for Real Pseudo Orthogonal Groups Sunil Mukhi and N. Mukunda	261
Bibliography for Part II Sunil Mukhi and N. Mukunda	273
BACK MATTER Sunil Mukhi and N. Mukunda	275
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