Operator regularization on the hypersphere
Operator regularization has proved to be a viable way of computing radiative corrections that avoids both the insertion of a regulating parameter into the initial Lagrangian and the occurrence of explicit infinities at any stage of the calculation. We show how this regulating technique can be used in conjunction with field theories defined on an n + 1-dimensional hypersphere, which is the stereographic projection of n-dimensional Euclidean space. The radius of the hypersphere acts as an infrared cutoff, thus eliminating the need to insert a mass parameter to serve as an infrared regulator. This has the advantage of leaving conformai symmetry present in massless theories, intact. We illustrate our approach by considering [Formula: see text], massless Yang–Mills gauge theories and the two-dimensional nonlinear bosonic sigma model with torsion. In the last model, the lowest mode is used as an infrared cutoff.