We consider two examples of symmetrical perturbation problems in several complex variables and show that special singularities appear. We then discuss the spectral properties of the perturbed operators in connection with the involved symmetries.
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.
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