On the Use of -Formalism of the Meson Field for Nuclear Interactions

Abstract

Following a method due to Harish-Chandra, a correspondence between the Proca and the ?-formalisms of the meson field theory is developed. An important feature of the method is that one can at any stage of calculations pass over from one formalism to the other. No explicit representation of the ?-matrices is required nor need one know the exact relationship between the elements of the wave function ? and the Proca field quantities U? and G??. This introduces considerable simplification in the introduction of nuclear interaction as compared with earlier treatments where one has to choose a special explicit representation of the ??'s and identify the various elements of the matrix ? with the components of U? and G??. The nuclear interaction is, in fact, here introduced very simply in an elegant way. The quantization is performed for the vector, scalar and pseudoscalar cases assuming in all cases both charge and dipole types of couplings. As an illustration of the method we calculate the scattering of positively charged mesons by protons. The spur calculations, so tedious in the earlier works, are now replaced by simple relations which are easily handled, and the results are obtained with about as much labour as is used in Proca's case with the additional advantage that both the longitudinal and the transverse parts of the meson field can here be treated together.