Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-02-04
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, revised version, title changed
Scientific paper
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 $t=T_1$ to $t=T_2$, where the interval $(T_1,T_2)$ 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 $\phi^4$ model in $R^{d+1}$. 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 $d\ge 6$).
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