1999/09/01 by Manfred Salmhofer, C. Wieczerkowski, Christian Wieczerkowski · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Convergence (economics) #Gaussian #Mathematical physics #Mathematics #Perturbation theory (quantum mechanics) #Physics #Propagator #Pure mathematics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Random Matrices and Applications #Renormalization #Simple (philosophy) #math-ph #math.MP
paper · pdf · doi:10.1023/a:1018661110470
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arxiv created 1999/09/01 · openalex publication_date 2000/04/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive norm bounds that imply the convergence of perturbation theory in fermionic quantum field theory if the propagator is summable and has a finite Gram constant. These bounds are sufficient for an application in renormalization group studies. Our proof is conceptually simple and technically elementary; it clarifies how the applicability of Gram bounds with uniform constants is related to positivity properties of matrices associated to the procedure of taking connected parts of Gaussian convolutions. This positivity is preserved in the decouplings that also preserve stability in the case of two-body interactions.