03376 - Differential Geometry and Lie Groups for Physicists [Fecko].pdf

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D I F F E R E N T I A L G E O M E T RY A N D L I E G RO U P S

FOR PHYSICISTS

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, including manifolds, tensor ﬁelds, differential

forms, connections, symplectic geometry, actions of Lie groups, bundles and spinors.

Having written it in an informal style, the author gives 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.

M a r i a n F e c k o

, currently at the Department of Theoretical Physics, Comenius Uni-

versity, Bratislava, Slovakia and at the Institute of Physics, Slovak Academy of Sciences,

Bratislava, works on applications of differential geometry in physics. He has over 15 years’

experience lecturing on mathematical physics and teaching courses on differential geometry

and Lie groups.

DIFFERENTIAL GEOMETRY AND LIE

GROUPS FOR PHYSICISTS

M A R I A N F E C KO

Comenius University, Bratislava, Slovakia

and

Slovak Academy of Sciences, Bratislava, Slovakia