Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

Details Momentum Space Regularizations and the Indeterminacy in the Schwinger Model Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

2009-10-22

arxiv.org/abs/0910.4322v1

Int.J.Mod.Phys.A26:1991-2006,2011

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, no figures

Scientific paper

10.1142/S0217751X11053067

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.

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