Bibliothèque de L'IMIST/CNRST

Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.

Companion volume to: Analysis, manifolds and physics. Rev. edition 1982.

Includes bibliographical references and index.

Description based on print version record.

Cover -- Preface to the second edition -- Preface -- Contents -- Conventions -- CHAPTER I. REVIEW OF FUNDAMENTAL NOTIONS OF ANALYSIS -- 1. Graded algebras -- 2. Berezinian -- 3. Tensor product of algebras -- 4. Clifford algebras -- 5. Clifford algebra as a coset of the tensor algebra -- 6. Fierz identity -- 7. Pin and Spin groups -- 8. Weyl spinors, helicity operator; Majorana pinors, charge conjugation -- 9. Representations of Spin(n, m), n + m odd -- 10. Dirac adjoint -- 11. Lie algebra of Pin(n, m) and Spin(n, m) -- 12. Compact spaces -- 13. Compactness in weak star topology -- 14. Homotopy groups, general properties -- 15. Homotopy of topological groups -- 16. Spectrum of closed and self-adjoint linear operators -- CHAPTER II. DIFFERENTIAL CALCULUS ON BANACH SPACES -- 1. Supersmooth mappings -- 2. Berezin integration; Gaussian integrals -- 3. Noether's theorems I -- 4. Noether's theorems II -- 5. Invariance of the equations of motion -- 6. String action -- 7. Stress-energy tensor; energy with respect to a timelike vector field -- CHAPTER III. DIFFERENTIABLE MANIFOLDS -- 1. Sheaves -- 2. Differentiable submanifolds -- 3. Subgroups of Lie groups. When are they Lie subgroups? -- 4. Cartan-Killing form on the Lie algebra g of a Lie group G -- 5. Direct and semidirect products of Lie groups and their Lie algebra -- 6. Homomorphisma and anthihomomorphisms of a life algebra into spaces of vector fields -- 7. Homogeneous spaces; symmetric spaces -- 8. Examples of homogeneous spaces, Stiefel and Grassmann manifolds -- 9. Abelian representations of nonabelian groups -- 10. Irreducibility and reducibility -- 11. Characters -- 12. Solvable Lie groups -- 13. Lie algebras of linear groups -- 14. Graded bundles -- CHAPTER IV. INTEGRATION ON MANIFOLDS -- 1. Cohomology. Definitions and exercises -- 2. Obstruction to the construction of Spin and Pin bundles; Stiefel-Whitney classes -- 3. Inequivalent spin structures -- 4. Cohomology of groups -- 5. Lifting a group action -- 6. Short exact sequence; Weyl Heisenberg group -- 7. Cohomology of Lie algebras -- 8. Quasi-linear first-order partial differential equation -- 9. Exterior differential systems -- 10. Bäcklund transformations for evolution equations -- 11. Poisson manifolds I -- 12. Poisson manifolds II -- 13. Completely integrable systems -- CHAPTER V. RIEMANNIAN MANIFOLDS. KÄHLERIAN MANIFOLDS -- 1. Necessary and sufficient conditions for Lorentzian signature -- 2. First fundamental form (induced metric) -- 3. Killing vector fields -- 4. Sphere Sn -- 5. Curvature of Einstein cylinder -- 6. Conformal transformation of Yang-Mills, Dirac and Higgs operators in d dimensions -- 7. Conformal system for Einstein equations -- 8. Conformal transformation of nonlinear wave equations -- 9. Masses of "homothetic" space-time -- 10. Invariant geometries on the squashed seven spheres -- 11. Harmonic maps -- 12. Composition of maps -- 13. Kaluz.

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