© 1984

Clifford Algebra to Geometric Calculus

A Unified Language for Mathematics and Physics


Part of the Fundamental Theories of Physics book series (FTPH, volume 5)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. David Hestenes, Garret Sobczyk
    Pages 1-43
  3. David Hestenes, Garret Sobczyk
    Pages 44-62
  4. David Hestenes, Garret Sobczyk
    Pages 63-136
  5. David Hestenes, Garret Sobczyk
    Pages 137-187
  6. David Hestenes, Garret Sobczyk
    Pages 188-224
  7. David Hestenes, Garret Sobczyk
    Pages 225-248
  8. David Hestenes, Garret Sobczyk
    Pages 249-282
  9. David Hestenes, Garret Sobczyk
    Pages 283-304
  10. Back Matter
    Pages 305-314

About this book


Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.


Fundamental theorem of calculus Vector space algebra derivative differential equation geometry mathematics transformation

Authors and affiliations

  1. 1.Department of PhysicsArizona State UniversityUSA
  2. 2.Institute for Theoretical PhysicsUniversity of WrocławPoland

About the authors

David Hesteness is awarded the Oersted Medal for 2002.
The Oersted Award recognizes notable contributions to the teaching of physics. It is the most prestigious award conferred by the American Association of Physics Teachers.

Bibliographic information

Industry Sectors
IT & Software


`... future authors will owe a great debt to Professors Hestenes and Sobczyk for this pioneering work.' Foundations of Physics, 16, 1986
`I repeat that GC enriches and simplifies everything it touches, not just on an advanced level but also, and perhaps even more so, on an elementary level. I am convinced that GC should be taught to undergraduate in place of the traditional approaches to vector algebra and analysis.' James S. Marsh in American Journal of Physics
`If the physics community seizes the opportunity represented by this book, and I hope it does, this book will become the handbook and the bible of GC.' American Journal of Physics, 53:5 (1985)