RELATIVISTIC QUANTIZATION AND IMPROVED EQUATION FOR A FREE RELATIVISTIC PARTICLE

Usually, the only difference between relativistic quantization and sta ndard quantization is that the Lagrangian of the system under consider ation should be Lorentz-invariant. The standard approaches are logical ly incomplete and produce solutions with unpleasant properties: negati ve energy and superluminal propagation. Furthermore, there is no unifi ed and natural procedure to obtain relativistic equations for differen t types of particles with the correct number of degrees of freedom. We propose a two-projection scheme of (special) relativistic quantizatio n. The first projection defines the quantization procedure (e.g., the Berezin-Toeplitz quantization). The second projection defines a causal structure of the relativistic system (e.g., the multiplication operat or by the characteristic function of the future cone). The two-project ion quantization introduces in a natural way the existence of three ty pes of relativistic particles (scalar, spinor, and 3-vector fields).