OKC/Nordita High-Energy Physics Theory seminar

Geometric Algebra as a coordinate free formalism for inner product spaces

by Timo Alho (University of Iceland)

122:026 ()


Geometric Algebra is the mathematical system defined by imbuing the vectors of an inner product space directly with the Clifford algebra generated by the inner product, without considering a separate representation of the algebra operating on the vectors. This simple change in point of view gives a system which generalizes exterior algebra, quaternions, spinors, and many other algebras used in theoretical physics, while simplifying both concepts and calculations. In this talk, we will mostly introduce the algebra, and it's extension to geometric calculus, before commenting on it's implications for physics and briefly mentioning our own work in the field.