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arXiv · 1110.1146

Convergence of quantum electrodynamics on the Poincare group

V. V. Varlamov
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Abstract

Extended particles are considered in terms of the fields on the Poincaré group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincaré group. Free fields of the spin 1/2 and 1 (Dirac and Maxwell fields) are considered in detail on the eight-dimensional homogeneous space, which is equivalent to a direct product of Minkowski spacetime and two-dimensional complex sphere. It is shown that a massless spin-1 field, corresponding to a photon field, should be defined within principal series representations of the Lorentz group. Interaction between spin-1/2 and spin-1 fields is studied in terms of a trilinear form. An analogue of the Dyson formula for $S$-matrix is introduced on the eight-dimensional homogeneous space. It is shown that in this case elements of the $S$-matrix are defined by convergent integrals.

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V. V. Varlamov. 2011-10-06. Convergence of quantum electrodynamics on the Poincare group. https://arxiv.org/abs/1110.1146

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