Quantum Mechanics in the Geometry of Space-Time

Beschreibung

This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered.The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.
This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered. The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.
Represents the most complete treatment of relativistic quantum mechanics in terms of real spacetime algebra Demonstrates practical advantages of STA theory Shows how to incorporate electroweak theory and gives novel insight into calculation of the Lamb shift, one of the pivotal problems in relativistic quantum theory

Autor*in

Roger Boudet

Themen in »Quantum Mechanics in the Geometry of Space-Time«

Algebraic Languages Clifford Algebra Dirac Theory of the Electron Euclidean space Gauge and the Yang-Mills Theory Glashow-Salam-Weinberg Electroweak Theory Isospin Matrices Minkowski Space-Time Quantum Electromagnetism Quantum Field Theory Spin and the Energy of a Particle

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From the reviews:

“This textbook addresses graduate students and researchers interested in quantum mechanics. … The author creates a very readable and well-accessible account of this new approach to quantum mechanics. … The basic endeavor of the book is a full translation of quantum mechanics into the real and invariant language of the Clifford algebra of space-time.” (Eckhard M. S. Hitzer, Mathematical Reviews, Issue 2012 m)

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