Abstract
We have constructed deformed scalar quantum electrodynamics where the scalar bosons are created and/or annihilated by the step operators of a generalized Heisenberg algebra and the photons are described in a standard way. One parameter, η, was introduced in those terms of the interaction Hamiltonian which have derivatives. We have computed the scattering process q-boson + photon →q-boson + photon up to second order in the coupling constant. We have found that the parameter, η, introduced is essential to preserve Lorentz and gauge invariance at the quantum level. We compare the cross-section for the scattering 2γ → q-boson +q-boson with the experimental data for 2γ → π+ + π−, where π± are the charged pions, obtaining good agreement in the region 0.55–0.7 GeV.
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