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 Smatrix in the current approximation is found. The unitarity of this operator is proven by the direct calculation.

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 arose 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. Canonical quantization of the system is performed. It is shown that the obtained conserved quantities and previously founded the Hamiltonian and the momentum of the system satisfy the commutational relations of the Poincaré group. The expression for S-matrix in the current approximation is found. Unitarity of this operator is proven by direct calculation.

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The Klein-Gordon field of imaginary mass is considered as a mediator of particle interaction. The static tachyon exchange potential is derived and its applied meaning is discussed. The Schrödinger equation with this potential is studied by means of variational and numerical methods. Conditions for existence of bound states are analyzed.