Physics – Mathematical Physics
Scientific paper
2004-07-20
J.Math.Phys. 46 (2005) 032301
Physics
Mathematical Physics
37 pages, v2 contains an improved treatment of the theta function in Appendix A.3
Scientific paper
10.1063/1.1839277
We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane (also known as noncommutative flat space). We also include a detailed comparison of our cut-off regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R^4 still holds if one replaces all pointwise products by the noncommutative Moyal product.
Loikkanen Juha
Paufler Cornelius
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