Consistent interactions between Yang-Mills gauge fields and an abelian 2-form are investigated by using a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and the BRST-invariant Hamiltonian of the uncoupled model generates the Yang-Mills Chern-Simons interaction term. The resulting interactions deform both the gauge transformations and their algebra, but not the reducibility relations.

Chern-Simons couplings between Yang-Mills gauge fields and an abelian 2-form are derived by means of cohomological arguments.

Consistent couplings among a set of scalar and vector fields in two dimensions are derived along a Hamiltonian BRST deformation procedure based on cohomological techniques. The resulting interactions deform both the gauge transformations and their algebra, and lead to a two-dimensional nonlinear gauge theory.

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By formulating the anomaly-free condition in terms of the fully symmetric third-order Casimir operators, we find all safe algebras and the algebraic equations satisfied by the highest weights of the anomaly-free representations of the only nonsafe algebras An, n≥2. By solving these equations for the irreducible representations of An−1 [SU(n)], n=3, 4, 5, and 6, we obtain the generating formulas of the highest weights for all anomaly-free representations of these groups. It turns out that for SU(n), n≥5 there is an infinite set of anomaly-free complex irreducible representations grouped as infinite series of such representations. Using the same technique, the infinite series of complex anomaly-free representations containing the lowest-dimension ones for SU(n), n=7, 8, 9, and 10 are determined.

The extremum properties of some functions defined on the compact groups or their representations are investigated. The extremum constraints for the vacuum expectation value of U(N) ×U(N) and SU(N) ×SU(N) ⧠ [Z2(P) ×Z2(C)] symmetry breaking perturbation Hamiltonian are used to determine the models compatible with nonnegative particle mass spectrum in the first perturbation order. Some model-independent properties inferred by extremum constraints of chiral and CP-symmetry breaking are also examined.