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出版社:世界圖書出版公司
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ISBN:9787510084423
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作者:(法)肖凱-布呂埃
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頁數:541
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出版日期:2015-01-01
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印刷日期:2015-01-01
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包裝:平裝
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開本:16開
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版次:1
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印次:1
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《分析流形和物理學》分為2卷,**卷1977年初版,之後7次重印或修訂。第2卷也在原來的基礎上做了不少改進,增加了一部分內容講述主纖維叢上的連通,包括完整,協變倒數,曲率,線性連通,示性類和不變曲率積分。書中有部分內容**重寫,增加了不少例子和練習,使得內容*加容易理解。 肖凱-布呂埃編寫的《分析流形和物理學(第2卷修訂版)(英文版)》為第2卷。
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Preface to the second edition Preface Contents Conventions 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 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 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 algebraof a Lie group G 5.Direct and semidirect products of Lie groups and their Lie algebra 6.Homomorphisms and antihomomorphisms of a Lie 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 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 (contributed by B. Kent Harrison) 10.Bicklund transformations for evolution equations (contributed by N.H. Ibragimov) 11.Poisson manifolds I 12.Poisson manifolds II (contributed by C. Moreno) 13.Completely integrable systems (contributed by C. Moreno) V. RIEMANNIAN MANIFOLDS. KAHLERIAN 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.Kaluza-Klein theories 14.Kihler manifolds; Calabi-Yau spaces V BIS. CONNECTIONS ON A PRINCIPAL FIBRE BUNDLE 1.An explicit proof of the existence of infinitely many connections on a principal bundle with paracompact base 2.Gauge transformations 3.Hopf fibering S3S2 4.Subbundles and reducible bundles 5.Broken symmetry and bundle reduction, Higgs mechanism 6.The Euler-Poincare characteristic 7.Equivalent bundles 8.Universal bundles. Bundle classification 9.Generalized Bianchi identity 10.Chern-Simons classes 11.Cocycles on the Lie algebra of a gauge group; Anomalies 12.Virasoro representation of(Diff Sl ). Ghosts. BRST operator VI. DISTRIBUTIONS 1.Elementary solution of the wave equation in d-dimensional spacetime 2.Sobolev embedding theorem 3.Multiplication properties of Sobolev spaces 4.The best possible constant for a Sobolev inequality on Rn, n > 3 (contributed by H. Grosse) 5.Hardy-Littlewood-Sobolev inequality (contributed by H. Grosse) 6.Spaces H,. 7.Spaces Hs(Sn) and H,., 8.Completeness of a ball on Wp in Ws 9.Distribution with laplacian in L2(In) 10.Nonlinear wave equation in curved spacetime 11.Harmonic coordinates in general relativity 12.Leray theory of hyperbolic systems. Temporal gauge in general relativity 13.Einstein equations with sources as a hyperbolic system 14.Distributions and analyticity: Wightman distributions and Schwinger functions (contributed by C. Doering) 15.Bounds on the number of bound states of the Schr6dinger operator 16.Sobolev spaces on Riemannian manifolds SUPPLEMENTS AND ADDITIONAL PROBLEMS 1.The isomorphism HHM4. A supplement to Problem 1.4 (I. 17) 2.Lie derivative of spinor fields (III.15) 3.Poisson-Lie groups, Lie bialgebras, and the generalized classical Yang-Baxter equation (IV. 14) (contributed by Carlos Moreno and Luis Valero) 4.Volume of the sphere Sn. A supplement to Problem V.4 (V. 15) 5.Teichmuller spaces (V.16) 6.Yamabe property on compact manifolds (V.17) 7.The Euler class. A supplement to Problem Vbis.6 (Vbis. 13) 8.Formula for laplacians at a point of the frame bundle (Vbis.14) 9.The Berry and Aharanov-Anandan phases (Vbis.15) 10.A density theorem. A supplement to Problem VI.6 "Spaces 11.Tensor distributions on submanifolds, multiple layers, and shocks (VI. 18) 12.Discrete Boltzrnann equation (VI. 19) Subject Index Errata to Part I
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