In view of an excellent agreement between the recently determinedv_μ-hadron couplings and predictions of the standard model, the basic question discussed is how far its neutral current predictions can be mimiced in going either from the isodoublet to an isotriplet (or an even higher isospin) left-handed representation or from SU_L (2) × U(1) toG × U(1), whereG is a simple group of rank two. This question is addressed with reference to a sufficiently broad class of schemes. Their most distinctive properties are: in the higher isospin scheme, neutrino couplings are precisely in the form obtainable with standard l.h. representation; the higher g.g. scheme isL+R type in which, to each light fermion of evenRU parity, a superheavy fermion of the same charge and oddRU parity is associated, parity conservation forbidding their mixing. Reasons for excluding theL-type andG₂ higher g.g. schemes are given. Their neutral current predictions are compared with those of the standard model. A higher isospin representation can mimic the predictions of the standard model in inclusive and semi-inclusivev_μ-hadron reactions but is conclusively discriminated from the isodoublet representation by elasticv_μ⁽⁻p scattering. TheG × U(1) scheme can mimic standard model neutrino sector but is conclusively discriminated from minimal scheme by parity violating effects.

In schemes with oneW boson and twoZ-bosons (mediating the charged and neutral current interactions involving ordinary fermions) based on the direct product and simple groups, SU(2) × U(1) ×u′(1) andG × U(1) (G is a simple group of rank two), the following two questions are discussed. (1) What are the necessary and sufficient conditions for minimal reducibility of the effective four-fermion neutral current interaction (involving ν_μ-hadron, electron-hadron and ν_μ-electron sectors) to the corresponding prediction of the standard model? (2) In what way are the masses of the twoZ-bosons constrained relative to the mass of the neutral boson of standard model? The answers to these questions are given first by keeping the underlying Higgs structure, responsible for gauge-boson (and fermion) mass generation, completely arbitrary (called Higgs-independent case) and then by making a specific choice for the Higgs structure resulting in a natural mass relation for theW andZ-bosons that is an exact counterpart toM_W^(S)/2=M_Z^(S)/2 sec²ϑ_W for the standard model (called Higgs-dependent case). The distinction between these two cases is brought out clearly as also that between the direct product and simple groups. Whether or not any assumption is made about the Higgs structure, with either the direct product or the simple group, it is concluded that in general there is aZ-boson lighter than the neutral boson of the standard model.

For each of a couple of two-dimensional forms for quark mass matrix, it is discussed how that form may be realised in a certain gauge scheme (one of them in the standard model and the other in a scheme based on simple rank two times U(1)) by imposing suitable discrete symmetries and how under a certain small angle approximation that form may be regarded as the simplest member of a family of higher dimensionality forms.

For Dynkin labels of weights in 5 and 10 of SU(5), 10 and 16 of SO(10) and 27 ofE, we find it instructive to (a) explōit the Cartan decom position into a nonsemi simple symmetric subalgebra and coset space, (b) introduce a set of annihilation and creation operators, that may act on an invariant 10>, to represent suitably the shift-action and weight-vectors.

The purpose of the paper is to construct a supersymmetric Lagrangian within the framework of classical mechanics which would be regarded as a candidate for passage to supersymmetric quantum mechanics.

The low energy effective scalar potential arising from the supergravity model proposed by Nilles, Srednicki and Wyler is minimized exactly. Bounds are derived for the parameters of the theory from the requirement that SU(2) × U(1) be broken at the tree level. These results support earlier approximate results.