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An Introduction to Covariant Quantum Mechanics

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  • 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

Part of the book series: Fundamental Theories of Physics (FTPH, volume 205)

  • 6347 Accesses

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  • ISBN: 978-3-030-89589-1
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Table of contents (31 chapters)

  1. Front Matter

    Pages i-xviii
  2. Introduction

    • Josef Janyška, Marco Modugno
    Pages 1-61
  3. Covariant Classical Mechanics

    1. Front Matter

      Pages 63-63
    2. Spacetime

      • Josef Janyška, Marco Modugno
      Pages 65-82
    3. Galilean Metric Field

      • Josef Janyška, Marco Modugno
      Pages 83-96
    4. Galilean Gravitational Field

      • Josef Janyška, Marco Modugno
      Pages 97-130
    5. Galilean Electromagnetic Field

      • Josef Janyška, Marco Modugno
      Pages 131-149
    6. Joined Spacetime Connection

      • Josef Janyška, Marco Modugno
      Pages 151-161
    7. Classical Dynamics

      • Josef Janyška, Marco Modugno
      Pages 163-180
    8. Sources of Gravitational and Electromagnetic Fields

      • Josef Janyška, Marco Modugno
      Pages 181-191
    9. Fundamental Fields of Phase Space

      • Josef Janyška, Marco Modugno
      Pages 193-209
    10. Geometric Structures of Phase Space

      • Josef Janyška, Marco Modugno
      Pages 211-221
    11. Hamiltonian Formalism

      • Josef Janyška, Marco Modugno
      Pages 223-242
    12. Lie Algebra of Special Phase Functions

      • Josef Janyška, Marco Modugno
      Pages 243-266
    13. Classical Symmetries

      • Josef Janyška, Marco Modugno
      Pages 267-276
  4. Covariant Quantum Mechanics

    1. Front Matter

      Pages 277-277
    2. Quantum Bundle

      • Josef Janyška, Marco Modugno
      Pages 279-293
    3. Galilean Upper Quantum Connection

      • Josef Janyška, Marco Modugno
      Pages 295-326
    4. Quantum Differentials

      • Josef Janyška, Marco Modugno
      Pages 327-353
    5. Quantum Dynamics

      • 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

  • Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Josef Janyška

  • 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.

Bibliographic Information

  • Book Title: An Introduction to Covariant Quantum Mechanics

  • Authors: Josef Janyška, Marco Modugno

  • Series Title: Fundamental Theories of Physics

  • DOI: https://doi.org/10.1007/978-3-030-89589-1

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-89588-4

  • eBook ISBN: 978-3-030-89589-1

  • Series ISSN: 0168-1222

  • Series E-ISSN: 2365-6425

  • Edition Number: 1

  • Number of Pages: XVIII, 838

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Quantum Physics, Classical Mechanics, Differential Geometry

Buying options

eBook
USD 189.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-89589-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD 249.99
Price excludes VAT (USA)