/* This is the header file for functions that allow to perform 
   vector calculus with complex four-vectors */

#ifndef fvec_h
#define fvec_h

#include <default.h>
#include <complex.h>
#include <vector.h>

typedef struct FVEC
{
     dcomplex fv[4];
} fvec;

typedef struct SPINOR_MAT
{
     dcomplex sm[4][4];  
} spinor_mat;


typedef struct SPINOR
{
     dcomplex s[4];  
} spinor;



fvec V4ini(dcomplex t, vec r);
fvec V4zero();
void V4echo( fvec a);

fvec V4add(fvec a, fvec b);
fvec V4sub(fvec a, fvec b);
dcomplex V4mul( fvec a, fvec b);

fvec V4conjg( fvec a);
fvec V4Rmul( fvec a, double b);
fvec V4Cmul( fvec a, dcomplex b);

double metric(int mu, int nu);
double antisymm_epsilon(int ka, int la, int mu, int nu);


spinor_mat SMadd(spinor_mat a, spinor_mat b);
spinor_mat SMsub(spinor_mat a, spinor_mat b);
spinor_mat SMRmul(spinor_mat a, double z);
spinor_mat SMCmul(spinor_mat a, dcomplex z);
spinor_mat SMmul(spinor_mat a, spinor_mat b);
spinor_mat SMmul3(spinor_mat a, spinor_mat b, spinor_mat c);
spinor_mat SMmul4(spinor_mat a, spinor_mat b, spinor_mat c, spinor_mat d);
spinor_mat SMmul5(spinor_mat a, spinor_mat b, spinor_mat c, 
                  spinor_mat d, spinor_mat e);

spinor_mat dirac_gamma(int mu);
spinor_mat dirac_gamma5();
spinor_mat dirac_sigma(int mu, int nu);
spinor_mat unit_spinor_mat();
spinor_mat zero_spinor_mat();

spinor_mat fvec_slash(fvec a);



spinor spinor_pos(vec p, double mass, double sproj);
spinor spinor_pos_xaxis(vec p, double mass, double sproj);
spinor spinor_pos_yaxis(vec p, double mass, double sproj);
spinor spinor_hel(vec p, double hel);
spinor spinor_anti_hel(vec p, double hel);
spinor spinor_part_hel(vec p, double mass, double hel);
spinor spinor_antipart_hel(vec p, double mass, double hel);

spinor spinor_adj(spinor a);
dcomplex spinleft_mat_spinright(spinor l, spinor_mat m, spinor r);


#endif