arXiv subjects
Publications and source records attributed to Boris Ivetic.
A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of noncomutativity: the Snyder model and the so called GUP models. For the Snyder model it is shown that all the amplitudes are finite at every order of the perturbation expansion.
A scalar field theory is constructed on an energy-momentum background of constant curvature. The generalization of the usual Feynamn rules for the flat geometry follows from the requirement of their covariance. The main result is that the invariant amplitudes are finite at all orders of the perturbation theory, due to the finitness of the momentum space. Finally, the relation with a field theory in spacetime representation is briefly discussed.
A geometrical interpretation of Schrödinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum space structure. Some specific examples are discussed in the context of flat space deformations and the Euclidean Snyder (spherical momentum space) model. In this formulation the dynamics for the deformations of the flat momentum space becomes trivial, while different versions of the Snyder model turn out to be dynamically equivalent.
We touch upon a long-standing question of the "true" one-dimensional hydrogen atom solution. From a symmetry point of view, Kepler problem in $d\ge2$ dimension is characterized by geometrical rotational symmetry, $SO(d)$, as well as dynamical, "accidental" $SO(d+1)$ symmetry. Because of topology, these two symmetries are mutually exclusive in one dimension, regardless of the regularization employed, drawing one to a conclusion that the question of "true" hydrogen atom in one dimension doesn't have an answer because a single dimension can not support both of the symmetries of Kepler problem. We argue our findings using a novel method to recover and classify solutions appearing in the literature according to the symmetry they respect. In particular, curious features of some of the solutions - double degeneracy and particle confinement - are directly attributed to the dynamical symmetry behind them.