Written in a quite formal mathematical way, by using the language of modern differential geometry
Contains a genuine learning program including modern differential geometry, classical mechanics, and quantum mechanics
Provides an appendix devoting to the exposition of some geometric methods
Table of contents (31 chapters)
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Front Matter
Pages i-xviii
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- Josef Janyška, Marco Modugno
Pages 1-61
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Covariant Classical Mechanics
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- Josef Janyška, Marco Modugno
Pages 65-82
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- Josef Janyška, Marco Modugno
Pages 83-96
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- Josef Janyška, Marco Modugno
Pages 97-130
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- Josef Janyška, Marco Modugno
Pages 131-149
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- Josef Janyška, Marco Modugno
Pages 151-161
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- Josef Janyška, Marco Modugno
Pages 163-180
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- Josef Janyška, Marco Modugno
Pages 181-191
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- Josef Janyška, Marco Modugno
Pages 193-209
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- Josef Janyška, Marco Modugno
Pages 211-221
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- Josef Janyška, Marco Modugno
Pages 223-242
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- Josef Janyška, Marco Modugno
Pages 243-266
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- Josef Janyška, Marco Modugno
Pages 267-276
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Covariant Quantum Mechanics
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Front Matter
Pages 277-277
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- Josef Janyška, Marco Modugno
Pages 279-293
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- Josef Janyška, Marco Modugno
Pages 295-326
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- Josef Janyška, Marco Modugno
Pages 327-353
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- Josef Janyška, Marco Modugno
Pages 355-411
About this book
This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.
Keywords
- Spacetime
- Galiean metric field
- Galiean gravitational field
- quantum bundle
- modern differential geometry
Authors and Affiliations
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Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
Josef Janyška
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Department of Mathematics and Informatics “U. Dini”, University of Florence, Florence, Italy
Marco Modugno
About the authors
Josef Janyška received his PhD in Geometry in 1984 from Charles University in Prague. From 1983 to 1991 he completed several study stays at the St. Petersburg University, the Lomonosov Moscow State University and the University of Florence. Since 1978 he worked at Masaryk University in Brno, first as an assistant professor and from 1988 as an associate professor. Since 2007 he is full Professor of Mathematics-Geometry at the Masaryk University in Brno. His primary research interests include the theory of natural and gauge-natural bundles and applications of differential geometric methods in theoretical physics.
Marco Modugno received his degree in Physics at University of Florence in 1966. Full professor of Mathematical Physics at Lecce University (1975-1979) and at Florence University (1979-2013). Currently, emeritus professor. Chief Editor of the "Journal of Geometry and Physics" (1982-2003), Editor of the Journal "Differential Geometry and its Applications" (1992-2016). Coordinator of the research group "Geometry and Physics" at University of Florence (1980-2013). His primary research interests deal with geometric approach to Mathematical Physics including General Relativity and Quantum Mechanics.