Geometric Algebra for Physicists Anthony Lasenby, Chris Doran
Publisher: Cambridge University Press
Mathematics for at least two centuries. As DSM notes below, I am not after the cross product calculation, but the geometric product calculation as found in geometric algebra. It is intended to be a set of HEP-specific foundation and utility classes such as random generators, physics vectors, geometry and linear algebra. Before that I should say a bit more about Clifford algebras. Ok, that's a semi-important point for the physicist; Clifford algebra is _a_ generalization of complex numbers and quaternions. Matrix representation for tridimensional space geometric algebra. Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics. Geometric algebra, or Clifford algebra, is a powerful mathematical language that contains vector algebra as a subsystem. The notorious way to use geometry in physics is by means of Gibbs' vector calculus, which became widespread in physical sciences and engineering. Francesco's notes about Maths, Physics, Computer Science Saturday, May 11, 2013. In my previous post I wrote about Geometric Algebra generalities. Learn Geometric Algebra and then you won't need complex numbers anymore (for physics) .. In the last three decades the development of a number of novel ideas in algebraic geometry, category . These are an important tool in many branches of mathematics - algebraic topology, K-theory, representation theory and in theoretical physics. What geometric product calculation? We saw that the tridimensional space generate a geometric algebra of dimension \(2^3 = 8 = 1 + 3 + 3 + 1\) composed of four linear spaces: scalars, vectors, bivectors and pseudo-scalars.