What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.
Uni10 /
RoadmapPending changes to the QuantumNumber library
class SU2 { public: SU2(); typedef half_int value_type; static double degree(half_int x); static double coupling_3j_phase(half_int a, half_int b, half_int c); // ... }; In the case of {$SU(2)$} the functions can be static because the symmetry group has no parameters. In the case of the Dihedral group {$D_n$} they cannot be static functions because the symmetry group depends on the parameter {$n$}. The representations of the dihedral group consist of two onedimensional reps {$+$} and {$$}; for {$n$} even there are also two onedimensional reps {$+n$} and {$n$}. The other reps {$j$} for {$0 < j < n$} are two dimensional. So a convenient representation is a 'signed' integer, where +0 and 0 are permissible values. (eg, this can be implemented using a sign bit or a 1's compliment representation.) We also allow halfinteger (projective) representations. Note: the halfinteger reps for odd {$n$} require complex coupling coefficients I think?!?! class Dihedral { public: Dihedral(int N_) : N(N_) {} typedef signed_half_int value_type; double degree(signed_half_int x) const; double coupling_3j_phase(signed_half_int a, signed_half_int b, signed_half_int c) const; // ... private: int N; };
