2011/04/30 by Walter D. van Suijlekom · 1 citation
Mathematics · Physics and Astronomy · #Action (physics) #BRST quantization #Background field method #Black Holes and Theoretical Physics #Dimensional regularization #Effective action #Gauge boson #Gauge fixing #Gauge theory #Hamiltonian lattice gauge theory #Introduction to gauge theory #Mathematical physics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Propagator #Quantum Electrodynamics and Casimir Effect #Quantum field theory #Quantum mechanics #Regularization (linguistics) #Renormalization #Supersymmetric gauge theory #Theoretical physics #Yang–Mills theory #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-012-1464-5
28 pages; revised version. To appear in CMP. arXiv admin note: substantial text overlap with arXiv:1101.4804
arxiv created 2011/11/16 · openalex publication_date 2012/03/23 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study renormalizability aspects of the spectral action for the Yang–Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting the latter as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the corresponding field theory can be renormalized by a simple shift of the spectral function appearing in the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator and compare to recent results in the literature.