|
Journal of Physical Studies 16(3), Article 3101 [10 pages] (2012)
DOI: https://doi.org/10.30970/jps.16.3101 PARTIALLY REDUCED FORMULATION OF SCALAR YUKAWA MODEL: POINCARÉ-INVARIANCE AND UNITARITYI. Zahladko, A. Duviryak
Institute for Condensed Matter Physics of NAS of Ukraine, Lviv, UA--79011, Ukraine, |
 |
We consider a scalar Yukawa-like model in the framework of partially reduced quantum field theory. The reduced Lagrangian of the model consists of free scalar field terms and nonlocal current interaction term. Hamiltonian expressions for conserved quantities arisen from a Lorentz-invariance of the model in the momentum representation have been found in the first-order approximation with respect to a coupling constant squared. The canonical quantization of the system is performed. It is shown that the obtained conserved quantities and the previously found Hamiltonian and momentum of the system satisfy the commutational relations of the Poincaré group. The expression for $S$-matrix in the current approximation is found. The unitarity of this operator is proven by the direct calculation.
PACS number(s): 11.10.Ef, 11.10.Lm, 11.30.Cp