Partial‐Wave Analysis in Terms of SL(2, C)/SU(2) Harmonic Functions

Awele Maduemezia
1969 Journal of Mathematical Physics  
A new scheme for analysing the scattering amplitude in the s-channel of a two-body elastic collision in terms of the representation functions of the covering group of the homogeneous Lorentz group is presented. The scheme uses representation functions defined on the homogeneous space SL(2, C)/SU(2), which for the equal mass case 2 2 2 considered here is the same as the hyperquadric q -q = -m , where m is the particle mass, q is the relative centre-of-mass momentum (in the initial or final
more » ... tial or final state) and 2q_ = f~s' is the centreof-mass energy. The corresponding representations are multivalued and belong to the so-called degenerate (but not most degenerate) series. The scattering amplitude derived has the correct threshold behaviour in the s-variable. HARMONIC FUNCTIONS 1.
doi:10.1063/1.1664870 fatcat:zuqju2aoofhudeekuy3isnbode