The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

We construct the general minimal coupling of N = 2 Yang-Mills fields to N = 2 sigma models in flat and curved harmonic superspace. We show that the complete symmetry group of the matter action can always be gauged in curved space. In flat space, we find that the gauging can be blocked by a local obstruction. We give a number of examples based on homogeneous quaternionic spaces and on quaternionic generalizations of the Taub-NUT and Eguchi-Hanson metrics.

Harmonic superspace is used to build up an unconstrained off-shell formulation of N=3 supersymmetry Yang-Mills theory. The theory is defined in an analytic N=3 superspace having M4(X)SU(3)/(U(1)(X)U(1)) as an even part. The basic objects are the analytic potentials which serve as gauge connections entering harmonic derivatives. The action is an integral over analytic superspace. The Lagrange density is surprisingly simple and it is gauge invariant up to total harmonic derivative. The equations of motion are integrability conditions on the internal space SU(3)/U(1)(X)U(1). It is the infinite set of auxiliary fields that allows the authors to overcome the 'N=3 barrier'.

The minimal N=1 supergravity with local U(1) invariance is analysed in the framework of complex superspace. The existence of a new geometric dimensionless scalar invariant is shown. It is not present in real superspace geometry. In order to write down an action this invariant must be constrained. The constraint can be implemented in the action by means of a Lagrange multiplier. A weaker constraint leads to an action with 16+16 fields.

A general method for deriving the superfield equations of motion is proposed. These equations contain the supplementary conditions of irreducibility with respect to the supersymmetry group. The method uses projection operators which single out the irreducible representations and especially the algebraic roots of these operators. It is found that the standard equations of motion for spin-vector and symmetric tensor fields can in fact be obtained by extracting the square roots of the projection operators for spin-3/2 and spin-2, respectively. The spinor superfield equation is deduced and discussed in detail.

Any gauge theory is proved to arise from spontaneous breakdown of symmetry under certain infinite parameter group, the corresponding gauge field being the Goldstone field by which this breakdown is accompanied.

Abstract It is shown that the available experimental data are equally consistent with spin-parity 0 − and 2 − of the X O (960) meson, but 2 − seems to be somewhat preferable. Both spin-parity alternatives, and new experiments to distinguish between them, are discussed.

It is remarked that the conventional effective Lagrangian with ρ and A1 mesons contains trilinear and quadrilinear derivative couplings. Thus one should add independently all terms with three and four field derivatives; the theory should then contain a number of arbitrary parameters. We suggest a new Lagrangian for the A1ρπ system containing no more than two field derivatives in each term. This model is determined by only four parameters gρ, gA, m ρ, MA and gives the smoothest momentum dependence for the contact vertices. We derive with necessity the reasonable value δ = −1 for the anomalous magnetic moment of A1 if the KSFR relation holds and also apply our model to ππ scattering and A1 decay.

The algebraic realization of Weinberg of the SU3 symmetry is considered. The necessity of nonets is motivated. The mass sum rules derived are satisfied to a great accuracy for the well established supermultiplets providing new predictions for nonets in which not all the members are established to date.