Physics – Mathematical Physics
Scientific paper
2007-11-14
J.Phys.Conf.Ser.128:012002,2008
Physics
Mathematical Physics
7 pages, no figures, talks given at the 5th International Symposium on "Quantum Theory and Symmetries", July 22-28, 2007, Vall
Scientific paper
10.1088/1742-6596/128/1/012002
Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j+1)-component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p_0^2 - p^2=M^2, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T-matrices for the fermion case and the boson case. However, certain differences are found. Possible physical applications are discussed.
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