2005/11/30 by Marco Frasca
Computer Science · Mathematics · Physics and Astronomy · #Classical limit #Coupling (piping) #Duality (order theory) #Field theory (psychology) #Harmonic oscillator #Lambda #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Order (exchange) #Perturbation theory (quantum mechanics) #Physics #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum field theory #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #cond-mat.other #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.73.027701
published as Phys.Rev.D73:027701,2006; Erratum-ibid.D73:049902,2006 · 6 pages, 4 figures. Version accepted for publication in Physical Review D. Added erratum to appear on PRD: just corrected eq.(5)
openalex publication_date 2006/01/05 · arxiv created 2006/01/26 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I analyze numerically a two-dimensional \ensuremathλ\ensuremathφ4 theory showing that in the limit of a strong coupling \ensuremathλ\ensuremath→\ensuremath∞ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M. Frasca, Phys. Rev. A 58, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this nonlinear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, I built a strongly coupled quantum field theory for a \ensuremathλ\ensuremathφ4 interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of space-time. The agreement with the Lehmann-K"allen representation of the perturbation series is then shown at the first order.