README

# Sa 26. Nov 16:45:30 EET 2011

 The gamma matrices.

 Standard choice (as in gwc):

 gamma_0:

 |  0  0 -1  0 |
 |  0  0  0 -1 |
 | -1  0  0  0 |
 |  0 -1  0  0 |

 gamma_1:

 |  0  0  0 -i |
 |  0  0 -i  0 |
 |  0 +i  0  0 |
 | +i  0  0  0 |

 gamma_2:

 |  0  0  0 -1 |
 |  0  0 +1  0 |
 |  0 +1  0  0 |
 | -1  0  0  0 |

 gamma_3:

 |  0  0 -i  0 |
 |  0  0  0 +i |
 | +i  0  0  0 |
 |  0 -i  0  0 |

 Permutation of the eight elements of a spinor (re0, im0, re1, im1, ...).


# Wed Nov 30 15:10:30 EET 2011
- gamma identification number:

  combination | g0 g1 g2 g3 id g5 g0g5 g1g5 g2g5 g3g5 g0g1 g0g2 g0g3 g1g2 g1g3 g2g3
  ---------------------------------------------------------------------------------
  id          |  0  1  2  3  4  5    6    7    8    9   10   11   12   13   14   15

- nomenclature: if i1 and not i2: id_full = id1
                if i2 and not i1: id_full = id2
                if i1 and i2    : id_full = ( id1 * 16 + id2 ) + 16

- isimag id: if i1 is imag: isimag_id += 1 
             if i2 is imag: isimag_id += 2

  (i.e.: isimag_id takes values 0, 1, 2 or 3)



GSL Bessel function

- include gsl_sf_bessel.h
- Function: double gsl_sf_bessel_j1 (double x)
- Function: int gsl_sf_bessel_j1_e (double x, gsl_sf_result * result)

GSL Spherical Harmonics

- include gsl_sf_legendre.h
- Function: double gsl_sf_legendre_sphPlm (int l, int m, double x)
- Function: int gsl_sf_legendre_sphPlm_e (int l, int m, double x, gsl_sf_result * result)

    These routines compute the normalized associated Legendre polynomial \sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x) suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x).