Supersymmetry for mathematicians : an introduction

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Supersymmetry for mathematicians : an introduction / V. S. Varadarajan

資料種別:: 図書
出版情報:: New York : Courant Institute of Mathematical Sciences, New York University
Providence, RI : American Mathematical Society, c2004
形態:: vii, 300 p. ; 26 cm
シリーズ名:: Courant lecture notes in mathematics ; 11 <BA42224256>
著者名:: Varadarajan, V. S. <DA00102918>
ISBN:: 9780821835746 [0821835742]
書誌ID:: BA68311108

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注記:

Includes bibliographical references

主題:

Supersymmetry

言語:

英語

目次情報:

Preface

Introduction / Chapter 1.：

Introductory Remarks on Supersymmetry / 1.1.：

Classical Mechanics and the Electromagnetic and Gravitational Fields / 1.2.：

Principles of Quantum Mechanics / 1.3.：

Symmetries and Projective Unitary Representations / 1.4.：

Poincare Symmetry and Particle Classification / 1.5.：

Vector Bundles and Wave Equations: The Maxwell, Dirac, and Weyl Equations / 1.6.：

Bosons and Fermions / 1.7.：

Supersymmetry as the Symmetry of a Z[subscript 2]-Graded Geometry / 1.8.：

References / 1.9.：

The Concept of a Supermanifold / Chapter 2.：

Geometry of Physical Space / 2.1.：

Riemann's Inaugural Talk / 2.2.：

Einstein and the Geometry of Spacetime / 2.3.：

Mathematical Evolution of the Concept of Space and Its Symmetries / 2.4.：

Geometry and Algebra / 2.5.：

A Brief Look Ahead / 2.6.：

Super Linear Algebra / 2.7.：

The Category of Super Vector Spaces / 3.1.：

The Super Poincare Algebra of Gol'fand-Likhtman and Volkov-Akulov / 3.2.：

Conformal Spacetime / 3.3.：

The Superconformal Algebra of Wess and Zumino / 3.4.：

Modules over a Supercommutative Superalgebra / 3.5.：

The Berezinian (Superdeterminant) / 3.6.：

The Categorical Point of View / 3.7.：

Elementary Theory of Supermanifolds / 3.8.：

The Category of Ringed Spaces / 4.1.：

Supermanifolds / 4.2.：

Morphisms / 4.3.：

Differential Calculus / 4.4.：

Functor of Points / 4.5.：

Integration on Supermanifolds / 4.6.：

Submanifolds: Theorem of Frobenius / 4.7.：

Clifford Algebras, Spin Groups, and Spin Representations / 4.8.：

Prologue / 5.1.：

Cartan's Theorem on Reflections in Orthogonal Groups / 5.2.：

Clifford Algebras and Their Representations / 5.3.：

Spin Groups and Spin Representations / 5.4.：

Spin Representations as Clifford Modules / 5.5.：

Fine Structure of Spin Modules / 5.6.：

The Central Simple Superalgebras / 6.1.：

The Super Brauer Group of a Field / 6.3.：

Real Clifford Modules / 6.4.：

Invariant Forms / 6.5.：

Morphisms from Spin Modules to Vectors and Exterior Tensors / 6.6.：

The Minkowski Signature and Extended Supersymmetry / 6.7.：

Image of the Real Spin Group in the Complex Spin Module / 6.8.：

Superspacetimes and Super Poincare Groups / 6.9.：

Super Lie Groups and Their Super Lie Algebras / 7.1.：

The Poincare-Birkhoff-Witt Theorem / 7.2.：

The Classical Series of Super Lie Algebras and Groups / 7.3.：

Superspacetimes / 7.4.：

Super Poincare Groups / 7.5.：

Preface

Introduction / Chapter 1.：

Introductory Remarks on Supersymmetry / 1.1.：

Classical Mechanics and the Electromagnetic and Gravitational Fields / 1.2.：

Principles of Quantum Mechanics / 1.3.：

Symmetries and Projective Unitary Representations / 1.4.：

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