Klein—Gordon—Dirac equation: Physical justification and quantization attempts

Discussed is the Klein—Gordon—Dirac equation, i.e. a linear differential equation with constant coefficients, obtained by superposing Dirac and dʹAlembert operators. A general solution of KGD equation as a superposition of two Dirac plane harmonic waves with different masses has been obtained. The multiplication rules for Dirac bispinors with different masses have been found. Lagrange formalism has been applied to receive the energy-momentum tensor and 4-current. It appears, in particular, that the scalar product is a superposition of Klein—Gordon and Dirac scalar products. The primary approach to canonical formalism is suggested. The limit cases of equal masses and one zero mass have been calculated.