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This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.
The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.
Contents:
Tensors
Algebraic Structures
Basic Group Concepts
Inner Products, Metrics, and Dual Spaces
Adjoints and Unitary Transformations
Eigenvalue Problems
Group Representation Theory
The Spherical Harmonics
The Representations of Semisimple Lie Algebras
Clifford Algebras
The Geometry of Lie Groups
Yang-Mills Equations
Riemannian Geometry
Characteristic Classes
and other topics
The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.
Contents:
Tensors
Algebraic Structures
Basic Group Concepts
Inner Products, Metrics, and Dual Spaces
Adjoints and Unitary Transformations
Eigenvalue Problems
Group Representation Theory
The Spherical Harmonics
The Representations of Semisimple Lie Algebras
Clifford Algebras
The Geometry of Lie Groups
Yang-Mills Equations
Riemannian Geometry
Characteristic Classes
and other topics