Eagle::STA Namespace Reference

Geometric algebra of spacetime, a.k.a. More...

Classes

• class CartesianChart4D
• class SphericalChart4D

Typedefs

• typedef CartesianChart4D::bivector bivector
• typedef Coordinates
  < CartesianChart4D<> >::Metric Metric
• typedef CartesianChart4D::point point
• typedef
  CartesianChart4D::pseudoscalar pseudoscalar4

  The 4-dimensional pseudoscalar i.
  

• typedef CartesianChart4D::trivector pseudovector
• typedef Coordinates
  < SphericalChart4D >::point sphericalpoint
• typedef Coordinates
  < SphericalChart4D >::vector sphericalvector
• typedef CartesianChart4D::trivector trivector
• typedef CartesianChart4D::vector vector

  4-Vectors in minkowskian space.
  

Functions

• template<class real > CartesianChart4D< real >::point operator+ (const typename CartesianChart4D< real >::vector &v, const typename CartesianChart4D< real >::point &P)

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Detailed Description

Geometric algebra of spacetime, a.k.a.

Spacetime Algebra (STA), by which we mean the Clifford algebara over Minkowskian, four-dimensional space.

http://arxiv.org/ftp/physics/papers/0511/0511247.pdf http://www.mrao.cam.ac.uk/~clifford/introduction/intro/node11.html

The STA has the structure 1 4 6 4 1, i.e. one scalar, four vectors, six bivectors, four tri-vectors and one pseudoscalar:

     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

Respectively, a bi-vector consists of 6 components, a tri-vector of four components and a vector of one component.

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Typedef Documentation

typedef CartesianChart4D ::pseudoscalar Eagle::STA::pseudoscalar4

The 4-dimensional pseudoscalar i.

The unit pseudoscalar obeys i*i=-1.

typedef CartesianChart4D ::vector Eagle::STA::vector

4-Vectors in minkowskian space.

The basis vectors are denoted by .