An Introduction to Covariant Quantum Mechanics

Josef Janyška, Marco Modugno (Autoren)

Buch | Softcover

XVIII, 838 Seiten

2023 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-89591-4 (ISBN)

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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.

lt;p>Josef Janyska 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 1978he 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 di erential 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 "Di erential 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.

Introduction.- Spacetime.- Galileian metric field.- Galileian gravitational field.- Galileian electromagnetic field.- Joined spacetime connection.- Classical dynamics.- Sources of gravitational and electromagnetic fields.- Fundamental fields of phase space.- Geometric structures of phase space.- Hamiltonian formalism.- Lie algebra of special phase functions.- Classical symmetries.- Quantum bundle.- Galileian upper quantum connection.- Quantum differentials.- Quantum dynamics.- Hydrodynamical picture of QM.- Quantum symmetries.- Quantum differential operators.- Quantum currents and expectation forms.- Sectional quantum bundle.- Feynman path integral.- Conclusions and further developments.- Examples.

"This book certainly makes a very valuable and original contribution to the literature on covariant quantum mechanics." (Frans Cantrijn, Mathematical Reviews, February, 2024)

Erscheinungsdatum	09.04.2023
Reihe/Serie	Fundamental Theories of Physics
Zusatzinfo	XVIII, 838 p. 10 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1288 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Galiean gravitational field • Galiean metric field • modern differential geometry • quantum bundle • Spacetime
ISBN-10	3-030-89591-2 / 3030895912
ISBN-13	978-3-030-89591-4 / 9783030895914
Zustand	Neuware