2010/02/04 by A. V. Stoyanovsky, Stoyanovsky, A. V. · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1002.0915
openalex publication_date 2010/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a conjectural way for computing the S-matrix and the correlation functions in quantum field theory beyond perturbation theory. The basic idea seems universal and naively simple: to compute the physical quantities one should consider the functional differential Schrodinger equation (without normal orderings), regularize it, consider the regularized evolution operator in the Fock space from t=T1 to t=T2, where the interval (T1,T2) contains the support of the interaction cutoff function, remove regularization (without adding counterterms), and tend the interaction cutoff function to a constant. We call this approach to QFT the No-Counterterm approach. We show how to compute the No-Counterterm perturbation series for the ϕ4 model in Rd+1. We give rough estimates which show that some summands of this perturbation series are finite without renormalization (in particular, one-loop integrals for d=3 and all integrals for d≥ 6).