© 2019

The Dirac Equation in Curved Spacetime

A Guide for Calculations


  • Many different approaches to calculate the Dirac equation in curved spacetime are fully discussed

  • The text is supported with several preparatory exercises and solutions

  • Some computational applications performed with the CARTAN software package are illustrated


Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Peter Collas, David Klein
    Pages 1-3
  3. Peter Collas, David Klein
    Pages 5-13
  4. Peter Collas, David Klein
    Pages 15-30
  5. Peter Collas, David Klein
    Pages 31-40
  6. Peter Collas, David Klein
    Pages 41-48
  7. Peter Collas, David Klein
    Pages 49-54
  8. Peter Collas, David Klein
    Pages 55-63
  9. Back Matter
    Pages 65-109

About this book


This book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.


Dirac Equation in Special Relativity Dirac Equation in General Relativity Gamma Matrices Spinorial Covariant Derivative CARTAN software Dirac Equation and curved graphene Fock-Ivanenko coefficients Newman-Penrose spin coefficients

Authors and affiliations

  1. 1.Department of Physics and AstronomyCalifornia State University, NorthridgeNorthridgeUSA
  2. 2.Department of Mathematics and Interdisciplinary Research Institute for the SciencesCalifornia State University, NorthridgeNorthridgeUSA

About the authors

Peter Collas is a professor emeritus of physics at California State University Northridge.  His current research interests are General Relativity theory and cosmology, with his investigations focussing on Dirac particles in gravitational waves, Fermi coordinates, as well as statistical mechanical problems in curved spacetime.

David Klein is a professor of mathematics at the California State University Northridge and is the director of the CSUN Climate Science Program. His research interests include mathematical physics, General Relativity and cosmology, statistical mechanics, mathematics education and climate change, a topic in which he has written the ebook, "Capitalism and Climate Change: The Science and Politics of Global Warming".

Bibliographic information

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“Ultimately, this short monograph will be of interest as a quick guide to researchers who need a notation reference, well organized overview of the literature, or an introduction to the subject, looking for connection with their own field; also for graduate students who are looking for a bird's eye view or need help with determining the learning path. It must be added that students especially will appreciate that the authors provide solutions to the exercises.” (Tomasz Artur Stachowiak, Mathematical Reviews, December, 2019)

“The book represents a very useful tool for graduate students and beginning researchers in a large area of the theory and applications of the Dirac equation. It can be useful for all the stages of learning: from the initial acknowledgement to deep investigations. … The book will be very useful to everybody desiring to make an economy with special articles from various journals.” (Alex B. Gaina, zbMath 1416.81003, 2019)