Eagle::STA Namespace Reference

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

Classes
class	CartesianChart4D
class	SphericalChart4D

Typedefs
typedef CartesianChart4D ::pseudoscalar	pseudoscalar4
	The 4-dimensional pseudoscalar i.
typedef CartesianChart4D ::vector	vector
	4-Vectors in minkowskian space.

Functions
double	norm (const PhysicalSpace::tvector &v)
	Compute the Euclidan norm of a vector.

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.

Typedef Documentation

pseudoscalar4

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

The 4-dimensional pseudoscalar i.

The unit pseudoscalar obeys i*i=-1.

vector

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

4-Vectors in minkowskian space.

The basis vectors are denoted by .

Function Documentation

norm()

double Eagle::norm ( const PhysicalSpace::tvector & v )

inline

Compute the Euclidan norm of a vector.

Note that if just the square of the norm is required, then function norm2() is more efficient since the square root does not need to be taken.