The Theory of Spinors
Elie Cartan
We have Weyl, Pauli, Dirac and Cartan to thank for our modern
theory of groups in physics. This book published in 1937
has none of the later Lie algebra representations of the Cartan generalization of groups
and thus, like Weyl's similar book may deceive the reader into thinking
he understands when he has only a rough and not very even
introduction to these groups. This book doesn't reach much higher than SU(2),
SO(3) and the Dirac U(1)*SU(2)*SU(2).
The standard model of physics deals with the symmetry breaking of SU(5)
( the Cartan A_4 group) to U(1)*SU(2)*SU(3). The Lie algebras and
irreducible Cartan representations of such higher symmetries
will demand the student read further than this text.
So this book is an historical introduction that gives the starting basis
for the mathematics needed by modern students in physics and chemistry.
