Vladimir V. Kisil, CINVESTAV del IPN (Mexico) and
Relativistic Quantization and Improved Equation
for a Free Relativistic Particle
(51K, LaTeX2e)
ABSTRACT. Usually the only difference between relativistic quantization and
standard one is that the Lagrangian of the system under consideration
should be Lorentz invariant.
The standard approaches are logically incomplete and produce
solutions with unpleasant properties: negative-energy, superluminal
propagation etc.
We propose a two-projections scheme of (special) relativistic
quantization. The first projection defines the quantization procedure
(e.g. the Berezin-Toeplitz quantization). The second
projection defines a casual structure of the relativistic system
(e.g. the operator of multiplication by the characteristic
function of the future cone).
The two-projections quantization introduces in a natural way the
existence of three types of relativistic particles
(with $0$, $\frac{1}{2}$, and $1$ spins).
Keywords: Quantization, relativity, spin, Dirac equation,
Klein-Gordon equation, electron, Segal-Bargmann space,
Berezin-Toeplitz quantization.
AMSMSC Primary: 81P10, 83A05; Secondary: 81R30, 81S99, 81V45