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Generalized Yang-Mills actions from Dirac operator determinants
KTH, Superseded Departments, Physics.
2001 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 11, 5238-5256 p.Article in journal (Refereed) Published
Abstract [en]

We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R-4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.

Place, publisher, year, edition, pages
2001. Vol. 42, no 11, 5238-5256 p.
URN: urn:nbn:se:kth:diva-21026ISI: 000171629200016OAI: diva2:339723
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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