Lectures on Differential Geometry of Modules and Rings: Application to Quantum Theory - Softcover

Sardanashvily, Gennadi

Softcover

ISBN 10: 3659238066 ISBN 13: 9783659238062

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

Differential geometry of smooth vector bundles can be formulated in algebraic terms of modules over rings of smooth functions. Generalizing this construction, one can define the differential calculus, differential operators and connections on modules over arbitrary commutative, graded commutative and non-commutative rings. For instance, this is the case of quantum theory, supergeometry and non-commutative geometry, respectively. The book aims to summarize the relevant material on this subject. Some basic applications to quantum theory are considered. The book is based on the graduate and post graduate courses of lectures given at the Department of Theoretical Physics of Moscow State University (Russia) and the Department of Mathematics and Physics of University of Camerino (Italy). It addresses to a wide audience of mathematicians, mathematical physicists and theoreticians.

About this title

About the Author

Gennadi Sardanashvily, theoretician and mathematical physicist, graduated from Moscow State University in 1973, Ph.D. (1980), D.Sc. (1998), Principal research scientist at the Department of Theoretical Physics of Moscow State University, published more than 300 scientific works and 22 text books and monographs.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• Language: English
• ISBN 10: 3659238066
• ISBN 13: 9783659238062
• Binding: Paperback
• Number of pages: 176