vsr_sta.h

/*

        space time algebra
    
        R1,3
        
 SEE Hestenes Space Time Algebra
*/
#include "detail/vsr_multivector.h"
 
namespace vsr{
        
        namespace sta {

    using algebra = algebra< metric<1,3>, double >;
         
                /*STANDARD FRAME of Orthonormal vectors decribes an Event ( time + location )
              An event, "proper vector" can be a proper momentum ( energy-momentum vector ) of a particle 
                  or a proper velocity
                */        
                                                        
                 //"Proper Vector"
                 using event = algebra::vec;
                
                 //Dirac Matrices are the Y . . . 
           using y0 = algebra::e<1>;                                                            //timelike observer (squares to 1) 
                                                                                                                          //forward light cone
           //Spacelike             
     using y1 = algebra::e<2>;                                          
                 using y2 = algebra::e<3>;                                               
                 using y3 = algebra::e<4>;                                              
                
                //Right-handed unit pseudoscalar
                 using I = algebra::blades<4>: 
       
                //individual position space vectors are made from spacetime bivectors yk^y0 
                // (considered "relative vectors..." -- relative to y0 . . . 
                //These generate G3 as G(P3)
                using O1 = typename OProd< Y1, Y0, Metric, false >::Type;       //yk^y0...
                using O2 = typename OProd< Y2, Y0, Metric, false >::Type;
                using O3 = typename OProd< Y3, Y0, Metric, false >::Type;  
                
                //Position space of observer y0
                using P3 = typename OProd< Event, Y0, Metric, false >::Type; 
                
                // SPLIT
                
                //a y0 spacetime split (time + position) is made from an observer's time axis Event * Y0 
                using Split = typename Prod< Event, Y0, Metric, false>::Type;      
                //lorentz-invariant means: independent of a chosen spacetime split

        }; 
                                                    
        
        typedef MGAMV< STA::Metric, STA::Vec > Vec; 
                
        typedef MGAMV< STA::Metric, STA::Sca > Sca; 
        typedef MGAMV< STA::Metric, STA::Y0 > Y0; 
        typedef MGAMV< STA::Metric, STA::Y1 > Y1;
        typedef MGAMV< STA::Metric, STA::Y2 > Y2;
        typedef MGAMV< STA::Metric, STA::Y3 > Y3;

        
        typedef MGAMV< STA::Metric, STA::O1 > O1;
        typedef MGAMV< STA::Metric, STA::O2 > O2;
        typedef MGAMV< STA::Metric, STA::O3 > O3;  
        
        typedef MGAMV< STA::Metric, STA::I > I;
        
        typedef MGAMV< STA::Metric, STA::P3 > P3;

        typedef MGAMV< STA::Metric, STA::Event > Event;
        
        typedef MGAMV< STA::Metric, STA::Split > Split;           
   
}

}