Linear Approximation for the Lorentz Gauge Field

Properties of the Lorentz gauge field in vacuum are examined in the free field approximation. We show that the Lorentz gauge field can be decomposed into six diagonalized fields, each of which obeys the Klein-Gordon equation and the irreducibility condition. We find that these diagonalized gauge fields can be massive, and that their spin and parity are 0+, 0−, 1+, 1−, 2+ and 2−. From the conditions for the Hamiltonian to be positive and for masses to be real, we get some restrictions on parameters appearing in the Lagrangian.