We report exact analytical expressions relating the fundamental parameters describing the neutralino sector in the context of the left-right supersymmetric model. The method used for such effects is the projector formalism deduced without taking into account the Jarlskog's projector formulas. Also, expressions for the neutralino masses and the neutralino mixing matrix are determined . The results are compared with numerical and analytical ones obtained in similar scenarios in the context of the minimal supersymmetric standard model.

The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the sh(2/2) superalgebra, also known as Heisenberg-Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2) + ⊃ sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg-Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and η-pseudo-superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.

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Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give rise to new classes of deformed coherent and squeezed states. They are parametrized by deformed algebra parameters and suitable redefinitions of them as paragrassmann numbers. Some properties of these deformed states also are analyzed. * email address: alvarez@dms.umontreal.ca

Analytical expressions relating the fundamental parameters describing the chargino sector in the context of the Left-Right Supersymmetric model are constructed. A general complex extension of the real non-symmetric chargino mass matrix including all possible CP-violating phases is considered. The method used for such a effects is the projector formalism based on the explicit knowledge of two unitary matrices diagonalizing the chargino mass matrix. Some possible scenarios allowing us to extract analytical and numerical values for the unknown parameters are considered. Moreover, an algorithm allowing us to disentangle the fundamental parameters of the chargino sector, based on possible measurements of some class of cross-section observables related to the chargino pair production in e + e − annihilation processes, is described. Some comparisons with the corresponding results in the context of the Minimal Supersymmetric Standard Model are given. *