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.

These course notes represent
Prof. Tisza's attempt at bringing conceptual clarity and unity to the
application and interpretation of advanced mathematical tools. In particular,
there is an emphasis on the unifying role that Group theory plays in classical,
relativistic, and quantum physics.

This
book covers the following topics: Basic Geometric Algebra, Geometric Calculus-
Derivative and Integration, Geometric Calculus on Manifolds, Multivector
Calculus, Multilinear Functions, Lagrangian and Hamiltonian Methods, Lie Groups
as Spin Groups and Classical Electromagnetic Theory.

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.