Coherent states and Green functions of relativistic quadratic systems

Explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method. The normal forms of the relativistic quadratic hamiltonians are briefly discussed. The important special cases, such as the motion of Dirac and Klein-Gordon charged particles in the fields of a plane wave and in the uniform electric and magnetic fields are investigated in detail.