On the Takahashi-Umezawa quantization of the external field problem for multi-mass fields

The Takahashi-Umezawa (Takahashi. An introduction to Field Quantization (Oxford, Pergamon. 1969). Takahashi and Umezawa. Nucl. Phys.; 51:193 (1964)) quantization method is applied to certain first-order equations which exhibit a mass spectra and have diagonalizable coefficient matrices. The Bhabha equations are a special case. It is shown that in all cases the independent field components satisfy the free field commutation rules in the presence of any external field. However, such theories have other difficulties. (author)