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Geometric Algebra for Physicists
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject withExpand
Gravity, gauge theories and geometric algebra
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independentExpand
New form of the Kerr solution
A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physicalExpand
A Bloch-sphere-type model for two qubits in the geometric algebra of a 6D Euclidean vector space
Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors.Expand
Lie-groups as Spin groups.
It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is availableExpand
A unified mathematical language for physics and engineering in the 21st century
This paper will chart the resurgence of the algebras of Clifford and Grassmann in the form of a framework known as geometric algebra (GA), and discuss whether it is indeed the unifying language for the physics and mathematics of the 21st century. Expand
This course introduces Geometric Algebra as a new mathematical technique to add to your existing base as a theoretician or experimentalist and develops applications of this new technique in the fields of classical mechanics, engineering, relativistic physics and gravitation. Expand
Imaginary numbers are not real—The geometric algebra of spacetime
This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a “geometric product” of vectors in 2-andExpand
Geometric algebra and its application to mathematical physics
Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the threeExpand
Geometric Algebra in Quantum Information Processing
This paper develops a geometric model for coupled two-state quan- tum systems (qubits) using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted asExpand