Book: D.J.H. Garling, Clifford Algebras: An Introduction


Description:
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell’s equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background – including multilinear algebra, quadratic spaces and finite-dimensional real algebras – easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.

Details:

  • Paperback: 208 pages
  • Publisher: Cambridge University Press (July 25 2011)
  • Language: English
  • ISBN-10: 1107422191
  • ISBN-13: 978-1107422193
  • Product Dimensions: 15.2 x 1.1 x 22.8 cm
  • Shipping Weight: 322 g

Full Table of Contents (PDF):
http://ebooks.cambridge.org/popups/pdf_viewer.jsf?cid=CBO9780511972997A004&ref=false&pubCode=CUP&urlPrefix=cambridge

Review:
“This is a notable book that constitutes a valuable addition to the library of anyone interested in the study of Clifford algebras and their applications. The book is written in a concise way and provides a precises introduction to the old and new developments concerning Clifford’s ideas. It can be used by either students or researchers in mathematics or physics who want to master this important subject.”
Pierre Angles, Mathematical Reviews

Table of Chapters:

Introduction:

pp. 1-4
Part One – The algebraic environment:

pp. 5-6
1 – Groups and vector spaces:

pp. 7-15
2 – Algebras, representations and modules:

pp. 16-35
3 – Multilinear algebra:

pp. 36-58
Part Two – Quadratic forms and Clifford algebras:

pp. 59-60
4 – Quadratic forms:

pp. 61-85
5 – Clifford algebras:

pp. 86-103
6 – Classifying Clifford algebras:

pp. 104-113
7 – Representing Clifford algebras:

pp. 114-136
8 – Spin:

pp. 137-152
Part Three – Some Applications:

pp. 153-154
9 – Some applications to physics:

pp. 155-163
10 – Clifford analyticity:

pp. 164-178
11 – Representations of Spind and SO(d):

pp. 179-185
12 – Some suggestions for further reading:

pp. 186-190
References:

pp. 191-192
Glossary:

pp. 193-196
Index:

pp. 197-200

Source: http://www.amazon.ca/Clifford-Algebras-Introduction-D-Garling/dp/1107422191, http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511972997&cid=CBO9780511972997A040

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