References
Here you can find useful references and bibliographic ressources related to our projects.
Geometric Algebra Primer
Jaap Suter — March 12, 2003
Adopted with great enthusiasm in physics, geometric algebra slowly emerges in computational science. Its elegance and ease of use is unparalleled. By introducing two simple concepts, the multivector and its geometric product, we obtain an algebra that allows subspace arithmetic. It turns out that being able to ‘calculate’ with subspaces is extremely powerful, and solves many of the hacks required by traditional methods. This paper provides an introduction to geometric algebra. The intention is to give the reader an understanding of the basic concepts, so advanced material becomes more accessible.
The Inner Products of Geometric Algebra
Leo Dorst — July, 2002
Making derived products out of the geometric product requires care in consistency. We show how a split based on outer product and scalar product necessitates a slightly different inner product than usual. We demonstrate the use and geometric significance of this contraction, and show how it simplifies treatment of meet and join. We also derive the sufficient condition for covariance of expressions involving outer and inner products.
Introduction aux Groupes de Lie destinée aux physiciens
F. Delduc
A representation of twistors within geometric (Clifford) algebra
Elsa Arcaute, Anthony Lasenby, Chris Doran
In previous work by two of the present authors, twistors were re-interpreted as 4-d spinors with a position dependence within the formalism of geometric (Clifford) algebra. Here we extend that approach and justify the nature of the position dependence. We deduce the spinor representation of the restricted conformal group in geometric algebra, and use it to show that the position dependence is the result of the action of the translation operator in the conformal space on the 4-d spinor. We obtain the geometrical description of twistors through the conformal geometric algebra, and derive the Robinson congruence. This verifies our formalism. Furthermore, we show that this novel approach brings considerable simplifications to the twistor formalism, and new advantages. We map the twistor to the 6-d conformal space, and derive the simplest geometrical description of the twistor as an observable of a relativistic quantum system. The new 6-d twistor takes the rôle of the state for that system. In our new interpretation of twistors as 4-d spinors, we therefore only need to apply the machinery already known from quantum mechanics in the geometric algebra formalism, in order to recover the physical and geometrical properties of 1-valence twistors.