Geometric Algebra and its Application to Mathematical Physics

Geometric Algebra and its Application to Mathematical Physics

Geometric Algebra and its Application to Mathematical Physics

This thesis is an investigation into the
properties and applications of Clifford’s geometric algebra. Topics covered
includes: Grassmann Algebra and Berezin Calculus, Lie Groups and Spin Groups,
Spinor Algebra, Point-particle Lagrangians, Field Theory, Gravity as a Gauge
Theory.

Author(s): Chris
J. L. Doran, Sidney Sussex College

This book covers the following
topics: The inner, outer, and geometric products, Geometric algebra in
Euclidean space, projections, reflections, and rotations, Frames and
bases, Linear algebra.

This note explains new techniques in Geometric Algebra
through their applications, rather than as purely formal mathematics. It
introduces Geometric Algebra as a new mathematical technique to add to your
existing base as a theoretician or experimentalist.

This note explans the following topics: Vector space Vn over scalars such
as IR, The clifford geometric products, Inner and outer products, Bivectors in
the standard model, Bivectors in the homogeneous model, Perpendicularity,
Reflection through communication, Duality and subspace representation.