Renormalization group for matrix models with branching interactions

We develop a method to obtain the large-N renormalization group flows for matrix models of two-dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one-matrix models. We show that it can be generalized to two-matrix models and we recover the Ising critical points.     

Asymptotic behaviour and reduction of couplings for models including nonrenormalizable interactions

We study equivalence relations among parametrizations of models including nonrenormalizable polynomial interactions. The method of reduction of couplings allows for a classification of the parameter associated to the nonrenormalizable perturbations and stability considerations. The relation to effective models is briefly discussed.     

Renormalization group equations and the continuum limit of some renormalizable quantum field theories

The renormalization group equations for asymptotically and non-asymptotically free theories are discussed by exploiting the general properties of their integral curves. Some constraints are derived on the existence of a consistent continuum limit for pure Yang-Mills theories in an infinite quantization volume. An analogy between the far infrared behaviour of non-abelian gauge theories and the deep ultraviolet one of asymptotically free theories is discussed.     

Renormalizability and nonrenormalizable interactions

Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.     

Renormalizability and nonrenormalizable interactions

Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.     

Remarks on nonrenormalizable interactions

It is argued that certain quantum field theories, including conventional nonrenormalizable theories, do not reduce to free theories when the interaction is turned off. The limiting, “pseudo-free” theories are formally characterized and suggested as alternative “unperturbed” theories possibly suitable for a meaningful perturbation analysis.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Local properties of nonrenormalizable interactions

The possibility of constructing strictly localizable fields is considered, using generalized S-type spaces as spaces of basis functions. The restrictions imposed on the asymptotic behavior of the amplitudes coincide with the well-known restrictions found by Jaffe. Contrary to previous results, the spatial amplitudes and momenta are regular, and not singular functions, in the case considered. The possibility of formulating spectral conditions is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 76–81, August, 1971.     

Renormalizable theories from nonrenormalizable interactions

By using Kikkawa’s method the equivalence of the nonrenormalizable pair interaction to a renormalizable theory is proved. Equivalence relationships between a few other nonrenormalizable and renormalizable interactions are also indicated.     

Vacuum configurations for renormalizable non-commutative scalar models

In this paper we find non-trivial vacuum states for the renormalizable non-commutative φ⁴ model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

A low temperature expansion for classicalN-vector models. II. Renormalization group equations

This paper continues the analysis of the low temperature expansions for classicalN-vector models started in [1]. A main part of it is a derivation of renormalization group equations and a construction of their solutions. To do this we have to introduce “a fluctuation integral” connected with a next renormalization transformation, and to make its preliminary analysis. The results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites, or actions described inductively in [1]. This work has been partially supported by the NSF Grant DMS-9102639.     

Renormalization group equations for a two-dimensional nonlinear sigma-model with torsion

The renormalization group equations in the one-loop approximation are formulated for a two-dimensional nonlinear -model with torsion on a semisimple group manifold. Solutions of these equations are investigated for several particular cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 37–40, September, 1988.     

Renormalization group equations for the Kobayashi-Maskawa matrix

The renormalization group equations for the parametrization-convention independent quadratic parameters |V _ij |² of the KM matrix are derived. Numerical analysis of these equations shows that the heavy quark family (t, b) tends to mix with the lighter families (c, s) and (u, d) with increasing energy, although the variation is very much slow. The CP-nonconservation effects are shown to get larger with energy.     

Renormalization group equations for effective field theories

We derive the renormalization group equations for a generic non-renormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral perturbation theory, e.g., this means that one can obtain the series of leading chiral logs by calculating only one-loop diagrams. We discuss also the renormalization group equations for the subleading divergences, and the crucial role of counterterms that vanish at the equations of motion. Finally, we show that the renormalization group equations obtained here apply equally well also to renormalizable theories.Received: 5 September 2003, Published online: 20 November 2003