C. de Calan

Local existence of the Borel transform in Euclidean φ 4 4

We bound rigorously the large order behaviour of φ44 euclidean perturbative quantum field theory, as the simplest example of renormalizable, but non-super-renormalizable theory. The needed methods are developed to take into account the structure of renormalization, which plays a crucial role in the estimates. As a main thorem, it is shown that the Schwinger functions at ordern are bounded byKnn!, which implies a finite radius of convergence for the Borel transform of the perturbation series.

A theorem on asymptotic expansion of Feynman amplitudes

For any Feynman amplitude, where any subset of invariants and/or squared masses is scaled by a real parameter λ going to zero or infinity, the existence of an expansion in powers of λ and lnλ is proved, and a method is given for determining such an expansion. This is shown quite generally in euclidean metric, whatever the external momenta (exceptional or not) and the internal masses (vanishing or not) may be, and for some simple cases in minkowskian metric, assuming only finiteness of the — eventually renormalized — amplitude before scaling. The method uses what is called “Multiple Mellin representation”, the validity of which is related to a “generalized power-counting” theorem.

Renormalization in the complete Mellin representation of Feynman amplitudes

The Feynman amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM integrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched.

Infrared- and ultraviolet-dimensional meromorphy of Feynman amplitudes

By the concurrent use of dimensional and analytic regularizations with the complete Mellin (CM) representation, we find in a direct way the ultraviolet and infrared poles in space-time dimension, for any Feynman amplitude with an arbitrary subset of vanishing masses.

The perturbation series for φ 3 4 field theory is divergent

We prove in a rigorous way the statement of the title.

Critical behavior of the compactified λϕ4 theory

We investigate the critical behavior of the N-component Euclidean λϕ4 model, in the large N limit, in three situations: confined between two parallel planes a distance L apart from one another; confined to an infinitely long cylinder having a square transversal section of area L2; and to a cubic box of volume L3. Taking the mass term in the form m02=α(T−T0), we retrieve Ginzburg–Landau models which are supposed to describe samples of a material undergoing a phase transition, respectively, in the form of a film, a wire and of a grain, whose bulk transition temperature (T0) is known. We obtain equations for the critical temperature as functions of L and of T0, and determine the limiting sizes sustaining the transition.

Critical properties of the topological Ginzburg-Landau model

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed-point structure and eventually the region of first-order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the

Radiative corrections to inelastic electron scattering with detection in coincidence — II

\ensuremath{\nu}

Local existence of the Borel transform in euclidean massless Φ 4 4

exponent does not vary very much from the

Infra-red divergence and incident photons

\mathrm{XY}