The Blau-Thompson N T = 2, D = 3 non-equivariant topological model, obtained through the so-called ,novel' twist of N = 4, D = 3 super Yang-Mills theory, is extended to a N T = 4, D = 3 topological theory. The latter, formally, may be regarded as a topological non-trivial deformation of the N T = 2, D = 4 Yamron-Vafa-Witten theory after dimensional reduction to D = 3. For completeness also the dimensional reduction of the half-twisted N T = 2, D = 4 Yamron model is explicitly constructed. 1

The osp(1, 2)-covariant Lagrangian quantization of irreducible gauge theories [1] is generalized to L-stage reducible theories. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case is discussed and Ward identities related to osp(1, 2) symmetry are given. Massive first-stage theories with closed gauge algebra are studied in detail. The generalization of the Chapline-Manton model and topological Yang-Mills theory to the case of massive fields is considered as examples.

The osp(1, 2)-covariant Lagrangian quantization of general gauge theories is formulated which applies also to massive fields. The formalism generalizes the Sp(2)covariant BLT approach and guarantees symplectic invariance of the quantized action. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case disappears in the limit m → 0. Ward identities related to osp(1, 2) symmetry are derived. Massive gauge theories with closed algebra are studied as an example.

A formulation of N T = 1, D = 8 Euclidean super Yang-Mills theory with generalized selfduality and reduced Spin(7)-invariance is given which avoids the peculiar extra constraints of Ref. [7]. Its reduction to seven dimensions leads to the G 2 -invariant N T = 2, D = 7 super Yang-Mills theory which may be regarded as a higher-dimensional analogue of the N T = 2, D = 3 super-BF theory. When reducing further that G 2 -invariant theory to three dimensions one gets the N T = 2 super-BF theory coupled a spinorial hypermultiplet.

Sp(2)-quantization of Batalin, Lavrov, and Tyutin has been extended to a formalism which is based on the orthosymplectic superalgebra osp(1,2) 8 and which can be applied to massive gauge theories. This is achieved by incorporating into the extended BRST transformations m-dependent terms in such a way that the m-extended ͑anti͒BRST symmetry of the quantum action W m is preserved. In that approach W m is required to satisfy the generalized a͒ Electronic