Dependence of variational perturbation expansions on strong-coupling behavior: Inapplicability ofδexpansion to field theory

2003/02/16 by B. Hamprecht, H. Kleinert · 2 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coupling (piping) #Exponent #Field (mathematics) #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Omega #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Philosophy #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #Statistical physics #hep-th

paper · pdf · doi:10.1103/physrevd.68.065001

published as Phys.Rev. D68 (2003) 065001 · Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/341

arxiv created 2003/02/16 · openalex publication_date 2003/09/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent \ensuremathω governing the approach to the strong coupling, or scaling, limit. Otherwise the procedure does not converge at all or to the wrong limit. This casts doubt on all papers applying the so-called \ensuremathδ expansion to quantum field theory.

Citations

• Critical exponents from seven-loop strong-couplingφ4theory in three dimensions
• Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases
• Critical exponents without β-function
• Convergence of the optimized δ expansion for the connected vacuum amplitude: Zero dimensions

Cited by

• Advances in perturbative thermal field theory
• Asymptotic properties of path integral ideals