A new formulation of quantum field theory on S4

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamentals constants. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper, a new formulation of field theory on a four-sphere is presented using the angular momentum space representation of SO(5). A review of field theory on a sphere is given and then show how a matrix element prescription in angular momentum space and a new summation technique based on the complex l-plane, overcome previous limitations in calculation techniques. The standard one-loop graphs of QED are given as examples. 13 refs., 3 figs