数学物理的几何方(影印版) 自然科学 (英)舒茨 新华正版
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作者(英)舒茨
出版社世界图书出版公司北京公司
ISBN9787510004513
出版时间2009-06
版次1
装帧平装
开本24开
页数264页
字数185千字
定价58元
货号xhwx_1202380455
上书时间2023-12-22
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目录：
1 some basic mathematics
1.1 the space rn and its topology
1.2 mappings
1.3 real analysis
1.4 group theory
1.5 linear algebra
1.6 the algebra of square matrices
1.7 bibliography
2 dffferentiable manifolds and tensors
2.1 defmition of a manifold
2.2 the sphere as a manifold
2.3 other examples of manifolds
2.4 global considerations
2.5 curves
2.6 functions on m
2.7 vectors and vector fields
2.8 basis vectors and basis vector fields
2.9 fiber bundles
2.10 examples of fiber bundles
2.11 a deeper look at fiber bundles
2.12 vector fields and integral curves
2.13 exponentiation of the operator d/dz
2.14 lie brackets and noncoordinate bases
2.15 when is a basis a coordinate basis？
2.16 one-forms
2.17 examples of one-forms
2.18 the dirac delta function
2.19 the gradient and the pictorial representation of a one-form
2.20 basis one-forms and ponents of one-forms
2.21 index notation
2.22 tensors and tensor fields
2.23 examples of tensors
2.24 ponents of tensors and the outer product
2.25 contraction
2.26 basis transformations
2.27 tensor operations on ponents
2.28 functions and scalars
2.29 the metric tensor on a vector space
2.30 the metric tensor field on a manifold
2.31 spe relativity
2.32 bibliography
3 lie derivatives and lie grou
3.1 introduction： how a vector field ma a manifold into itself
3.2 lie dragging a function
3.3 lie dragging a vector field
3.4 lie derivatives
3.5 lie derivative of a one-form
3.6 submanifolds
3.7 frobenius theorem (vector field version)
3.8 proof of frobenius theorem
3.9 an example： the generators ors2
3.10 invariance
3.11 killing vector fields
3.12 killing vectors and conserved quantities in particle dynamics
3.13 aal symmetry
3.14 abstract lie grou
3.15 examples of lie grou
3.16 lie algebras and their grou
3.17 realizations and representatidns
3.18 spherical symmetry， spherical harmonics and representations of the rotation group
3.19 bibliography
4 differential forms a the algebra and integral calculus of forms
4.1 definition of volume - the geometrical role of differential forms
4.2 notation and definitions for antisymmetric tensors
4.3 differential forms
4.4 manipulating differential forms
4.5 restriction of forms
4.6 fields of forms
4.7 handedness and orientability
4.8 volumes and integration on oriented manifolds
4.9 n-vectors， duals， and the symbol
4.10 tensor densities
4.11 generalized kronecker deltas
4.12 determinants and
4.13 metric volume elements b the differential calculus of forms and its applications
4.14 the exterior derivative
4.15 notation for derivatives
4.16 familiar examples of exterior differentiation
4.17 integrability conditions for partial differential equations
4.18 exact forms
4.19 proof of the local exactness of closed forms
4.20 lie derivatives of forms
4.21 lie derivatives and exterior derivatives mute
4.22 stokes theorem
4.23 gauss theorem and the definition of divergence
4.24 a glance at cohomology theory
4.25 differential forms and differential equations
4.26 frobenins theorem (differential forms version)
4.27 proof of the equivalence of the two versions of frobenius theorem
4.28 conservation laws
4.29 vector spherical harmonics
4.30 bibliography
5 applications in physics a thermodynamics
5.1 simple systems
5.2 maxwell and other mathematical identities
5.3 ite thermodynamic systems： caratheodorys theorem b hamilton/an mechanics
5.4 hamiltodian vector fields
5.5 canonical transformations
5.6 map between vectors and one-forms provided by
5.7 poisson bracket
5.8 many-particle systems： symplectic forms
5.9 linear dynamical systems： the symplectic inner product and conserved quantities
5.10 fiber bundle structure of the hamiltonian equations c electromagism
5.11rewriting maxwells equations using differential forms
5.12 charge and topology
5.13 the vector potential
5.14 ne waves： a simple example d dynamics of a perfect fluid
5.15 role of lie derivatives
5.16 the oving time-derivative
5.17 equation of motion
5.18 conservation of vorticity
e cosmology
5.19 the cosmological principle
5.20 lie algebra of mamal symmetry
5.21 the metric of a spherically symmetric three-space
5.22 construction of the six killing vectors
5.23 open， closed， and flat universes
5.24 bibliography
6 connections for riemnnnian manifolds and gauge theories
6.1 introduction
6.2 parallelism on curved surfaces
6.3 the covariant derivative
6.4 ponents： covariant derivatives of the basis
6.5 torsion
6.6 geodesics
6.7 normal coordinates
6.8 riemann tensor
6.9 geometric interpretation of the riemann tensor
6.10 flat spaces
6.11 patibility of the connection with volume-measure or the metric
6.12 metric connections
6.13 the affine connection and the equivalence principle
6.14 connections and gauge theories： the example of electromagism
6.15 bibfiography
appendix： solutions and hints for selected exercises
notation
index
内容简介：
现代微分几何在理论物理中扮演着重要的角，并且在相对论、宇宙学、高能量物理和场论、热动力学、流体力学以及力学中的应用也益突显。本书作为一本微分几何教程，介绍了李导数、李群以及微分形式的引入方，及其在理论物理中的广泛应用。有物理和应用数学背景的读者学完本书，可以更深入学一些科研文献以及更高层次的纯数学理论。
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