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Yang-Mills action from minimally coupled bosons on R-4 and on the four-dimensional Moyal plane
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2005 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 3, 032301- p.Article in journal (Refereed) Published
Abstract [en]

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 cutoff 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 R-theta(4) We also include a detailed comparison of our cutoff 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.

Place, publisher, year, edition, pages
2005. Vol. 46, no 3, 032301- p.
Keyword [en]
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URN: urn:nbn:se:kth:diva-37820DOI: 10.1063/1.1839277ISI: 000227949000011ScopusID: 2-s2.0-17744372542OAI: diva2:437584
QC 20110830Available from: 2011-08-30 Created: 2011-08-17 Last updated: 2011-08-30Bibliographically approved

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