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Differential geometry and lie groups for physicists /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Differential geometry and lie groups for physicists // Marián Fecko.
其他題名:	Differential Geometry & Lie Groups for Physicists
作者:	Fecko, Marián,
面頁冊數:	1 online resource (xv, 697 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Mathematical physics. -
電子資源:	https://doi.org/10.1017/CBO9780511755590
ISBN:	9780511755590 (ebook)

Differential geometry and lie groups for physicists /
Fecko, Marián,

Differential geometry and lie groups for physicists /Differential Geometry & Lie Groups for PhysicistsMarián Fecko. - 1 online resource (xv, 697 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

The concept of a manifold --Preface --

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

ISBN: 9780511755590 (ebook)Subjects--Topical Terms:

527831
Mathematical physics.

LC Class. No.: QC20.7.D52 / F43 2006

Dewey Class. No.: 530.15636

Differential geometry and lie groups for physicists /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 2 0 $g Preface -- $g Introduction -- $t The concept of a manifold -- $t Vector and tensor fields -- $t Mappings of tensors induced by mappings of manifolds -- $t Lie derivative -- $t Exterior algebra -- $t Differential calculus of forms -- $t Integral calculus of forms -- $t Particular cases and applications of Stokes' theorem -- $t Poincaré lemma and cohomologies -- $t Lie groups: basic facts -- $t Differential geometry on lie groups -- $t Representations of Lie groups and Lie algebras -- $t Actions of Lie groups and Lie algebras on manifolds -- $t Hamiltonian mechanics and symplectic manifolds -- $t Parallel transport and linear connection of M.
505 0 0 $t Field theory and the language of forms -- $t Differential geometry on T M and T* M -- $t Hamiltonian and Lagrangian equations -- $t Linear connection and the frame bundle -- $t Connection on a principal G-bundle -- $t Gauge theories and connections -- $t Spinor fields and the Dirac operator -- $g Appendix $t A Some relevant algebraic structures -- $g Appendix B $t Starring.
520 $a Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.
650 0 $a Mathematical physics. $3 527831
650 0 $a Lie groups. $3 527929
650 0 $a Geometry, Differential. $3 527830
776 0 8 $i Print version: $z 9780521845076
856 4 0 $u https://doi.org/10.1017/CBO9780511755590