International Journal of Modern Physics A

We review developments in top condensation starting from the first example which was a simple effective Nambu–Jona-Lasinio (NJL) model. The connection between the underlying four-fermion interaction and the structure of the composite Higgs sector is generalized to obtain the scalar sectors of a number of Standard Model extensions dynamically from some NJL model, as well as to include possible radial and spin excitations of the Higgs sector. In all these NJL models the symmetries do not forbid further higher dimensional four-fermion operators. If such operators could have arbitrary strength then this would result in arbitrary Higgs and top mass predictions. The nonrenormalizable NJL model is however thought to be only an effective description of some fully consistent theory where higher dimensional operators are not free parameters so that the corresponding four-fermion operators are restricted. We discuss renormalizable gauge theories of top condensation where this is the case. These models are therefore predictive and do not lead to arbitrary predictions.

The results of Ref. 1 are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The As operation for integrals is defined and a simple combinatorial technique is developed to study its exponentiation. The As operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance, operator-product expansions, the decoupling theorem etc.: e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R operation is constructed. The results are valid for arbitrary QFT models.

The effects of short range correlations for two nucleon emission in peripheral relativistic heavy ion collisions are investigated. The cross section is calculated in Born approximation with properly orthogonalized initial and final states.

We obtain the double scaling limit of a set of superloop equations recently proposed to describe the coupling of two-dimensional supergravity to minimal superconformal matter of type (2,4m). The continuum loop equations are described in terms of a theory with a Z₂-twisted scalar field and a Weyl–Majorana fermion in the Ramond sector. We have computed correlation functions in genus zero, one and partially in genus two. An integrable supersymmetric hierarchy describing our model has not yet been found. We present a heuristic argument showing that the purely bosonic part of our model is described by the KdV hierarchy.

A generalized version is proposed for the field–antifield formalism. The antibracket operation is defined in arbitrary field–antifield coordinates. The antisymmetric definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate–invariant way. The general hypergauge functions are shown to be antisymmetric first–class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones.