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理論工作者的高等微分幾——纖維叢、射流流形和拉格朗日理論(英文) 版權信息
- ISBN：9787560343976
- 條形碼：9787560343976 ; 978-7-5603-4397-6
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
理論工作者的高等微分幾——纖維叢、射流流形和拉格朗日理論(英文) 內容簡介
本書是一部英文版的數學專著。與量子場論不同的是,經典場論可以用嚴格的數學方式表述,將經典場視為光滑纖維叢的截面.對于R上的纖維叢,不定常的非相對論力學也是如此.本書旨在匯編有關纖維叢、射流流形、聯絡、分次流形和拉格朗日理論的相關材料。本書以莫斯科國立大學(俄羅斯)理論物理系的本科生和研究生課程為基礎。
理論工作者的高等微分幾——纖維叢、射流流形和拉格朗日理論(英文) 目錄
Introduction
1 Geometry of fibre bundles
1．1 Fibre bundles
1．2 Vector and affine bundles
1．3 Vector fields
1．4 Exterior and tangent-valued forms
2 Jet manifolds
2．1 First order jet manifolds
2．2 Higher order jet manifolds
2．3 Differential operators and equations
2．4 Infinite order jet formalism
3 Connections on fibre bundles
3．1 Connections as tangent-valued forms
3．2 Connections as jet bundle sections
3．3 Curvature and torsion
3．4 Linear and affine connections
3．5 Flat connections
3．6 Connections on composite bundles
4 Geometry of principal bundles
4．1 Geometry of Lie groups
4．2 Bundles with structure groups
4．3 Principal bundles
4．4 Principal connections
4．5 Canonical principal connection
4．6 Gauge transformations
4．7 Geometry of associated bundles
4．8 Reduced structure
5 Geometry of natural bundles
5．1 Natural bundles
5．2 Linear world connections
5．3 Affine world connections
6 Geometry of graded manifolds
6．1 Grassmann-graded algebraic calculus
6．2 Grassmann-graded differentialcalculus
6．3 Graded manifolds
6．4 Graded differential forms
7 Lagrangian theory
7．1 Variational bicomplex
7．2 Lagrangian theory on fibre bundles
7．3 Grassmann-graded Lagrangian theory
7．4 Noether identities
7．5 Gauge symmetries
8 Topics on commutative geometry
8．1 Commutative algebra
8．2 Differentialoperators on modules
8．3 Homology and cohomology of complexes
8．4 Differential calculus over a commutative ring
8．5 Sheaf cohomology
8．6 Local-ringed spaces
Bibliography
Index
編輯手記
1 Geometry of fibre bundles
1．1 Fibre bundles
1．2 Vector and affine bundles
1．3 Vector fields
1．4 Exterior and tangent-valued forms
2 Jet manifolds
2．1 First order jet manifolds
2．2 Higher order jet manifolds
2．3 Differential operators and equations
2．4 Infinite order jet formalism
3 Connections on fibre bundles
3．1 Connections as tangent-valued forms
3．2 Connections as jet bundle sections
3．3 Curvature and torsion
3．4 Linear and affine connections
3．5 Flat connections
3．6 Connections on composite bundles
4 Geometry of principal bundles
4．1 Geometry of Lie groups
4．2 Bundles with structure groups
4．3 Principal bundles
4．4 Principal connections
4．5 Canonical principal connection
4．6 Gauge transformations
4．7 Geometry of associated bundles
4．8 Reduced structure
5 Geometry of natural bundles
5．1 Natural bundles
5．2 Linear world connections
5．3 Affine world connections
6 Geometry of graded manifolds
6．1 Grassmann-graded algebraic calculus
6．2 Grassmann-graded differentialcalculus
6．3 Graded manifolds
6．4 Graded differential forms
7 Lagrangian theory
7．1 Variational bicomplex
7．2 Lagrangian theory on fibre bundles
7．3 Grassmann-graded Lagrangian theory
7．4 Noether identities
7．5 Gauge symmetries
8 Topics on commutative geometry
8．1 Commutative algebra
8．2 Differentialoperators on modules
8．3 Homology and cohomology of complexes
8．4 Differential calculus over a commutative ring
8．5 Sheaf cohomology
8．6 Local-ringed spaces
Bibliography
Index
編輯手記
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