Wigner.h

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#ifndef AMPGEN_WIGNER_H
#define AMPGEN_WIGNER_H
#include "AmpGen/Expression.h"
#include "AmpGen/Tensor.h"
#include "AmpGen/Particle.h"
#include "AmpGen/Transform.h"
 
namespace AmpGen {
  class Particle;
  using TransformCache = std::map<std::string, TransformSequence>;
 
  Expression wigner_d( const Expression& cb, const double& j, const double& m, const double& n );
  Expression wigner_D( const std::pair<Expression, Expression>& P, const double& J, const double& lA, const double& lB, DebugSymbols* db);
  double CG( const double& j1,
      const double& m1,
      const double& j2, 
      const double& m2,
      const double& J,
      const double& M );

  TransformSequence wickTransform(const Tensor& P, const Particle& p, const int& ve =1, DebugSymbols* db = nullptr );   
 
  Expression helicityAmplitude(const Particle& particle, 
                               const TransformSequence& parentFrame, 
                               const double& Mz,    
                               DebugSymbols* db , 
                               const int sgn=1, 
                               TransformCache* cacheptr = nullptr); 
  Tensor basisSpinor(const int& polState, const int& id);
  Tensor basisVector(const int& polState);
 
  struct LS {
    double factor = {1};
    double cg1    = {0};
    double cg2    = {0};
    double p      = {0}; 
    double m1     = {0};
    double m2     = {0};
  };
 
  std::vector<LS> calculate_recoupling_constants( 
      const double& J, 
      const double& M,
      const double& L, 
      const double& S,
      const double& j1,
      const double& j2 );
}
 
#endif