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Hadron-nucleus amplitudes at high energies are studied in the toy Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.
The effective reggeon field theory in zero transverse dimension (the toy model) is studied. The transcendental equation for eigenvalues of the Hamiltonian of this theory is derived and solved numerically. The found eigenvalues are used for the calculation of the pomeron propagator.
We propose the one-dimensional reggeon theory describing local pomerons and odderons. It generalizes the well-known one-dimensional theory of pomerons (the Gribov model) and includes only triple interaction vertices. The proposed theory is studied by
We discuss renormalization in a toy model with one fermion field and one real scalar field phi, featuring a spontaneously broken discrete symmetry which forbids a fermion mass term and a phi^3 term in the Lagrangian. We employ a renormalization schem
Fundamental inequalities for QCD sum-rules are applied to resolve a paradox recently encountered in a sum-rule calculation. This paradox was encountered in a toy model known to be free of resonances that yields an apparent resonance using a standard
In an attempt to regularize a previously known exactly solvable model [Yang and Zhang, Eur. J. Phys. textbf{40}, 035401 (2019)], we find yet another exactly solvable toy model. The interesting point is that while the Hamiltonian of the model is param