Strong coupling limit of gφ4 theory: General formalism and applications

A method, independently proposed by Kaiser and by us, to study the strong coupling limit of the Green functions is described and discussed. Although its quantum mechanical version exhibits unusual features, an application to the anharmonic oscillator indicates that the method is able to reproduce correctly known numerical results. In spite of difficulties in the setting up of a renormalization program for the theory, a preliminary study of the CS β function for the gφ⁴ interaction shows that $\text{β(g}{}_{\mathrm{<mtext>r</mtext>}}$ is asymptotically linear in the renormalization coupling constant. Evidence is given for the compatibility of this behaviour with the information that can be drawn from the known perturbative expansion.     

Characteristic cohomology ofp-form gauge theories

The characteristic cohomologyH ^k _char(d) for an arbitrary set of freep-form gauge fields is explicitly worked out in all form degreesk < n — 1, wheren is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interactingp-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.     

BRST Cohomology of the Chapline–Manton Model

We completely compute the local BRST cohomology H(s|d) of the combined Yang–Mills 2-form system coupled through the Yang–Mills Chern–Simons term (Chapline–Manton model). We consider the case of a simple gauge group and explicitly include in the analysis the sources for the BRST variations of the fields (antifields). We show that there is an antifield independent representative in each cohomological class of H(s|d) at ghost number 0 or 1. Accordingly, any counterterm may be assumed to preserve the gauge symmetries. Similarly, there is no new candidate anomaly beside those already considered in the literature, even when one takes the antifields into account. We then characterize explicitly all the nontrivial solutions of the Wess–Zumino consistency conditions. In particular, we provide a cohomological interpretation of the Green–Schwarz anomaly cancellation mechanism.     

Strong coupling limit of the gφ4 theory

The strong coupling limit of the gφ⁴ theory in the framework of the path integral formalism. An expansion of the Green's functions in negative powers of the coupling constant is obtained; at each order the dependence on the external momenta is of polynomial type. A renormalization procedure is proposed; the asymptotic behaviour of the Callan-Symanzik β function is studied and the existence of a stable ultraviolet fixed point is established.     

Integral relation for the t-dependence of the It = 1 ππ absorptive part

We derive a sum rule relating the I_t = 1 ππ absorptive part Δ(s, t) to integrals over total cross sections. We show how it can be used to estimate the t-dependence of this absorptive part and in particular its zero. A recent low energy ππ phenomenological analysis seems to imply a zero near t = ?0.2 GeV² for large s.