SUSY transformations with complex factorization constants. Application to spectral singularities

Supersymmetric (SUSY) transformation operators corresponding to complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. Obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of selfadjoint operators. A new regularization procedure for the resolution of the identity operator in terms of continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also shown that the continuous spectrum eigenfunction has zero binorm (in the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte

Wess-Zumino term in the N=4 SYM effective action revisited

The low-energy effective action for the N=4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU(4) R-symmetry, we find a four-dimensional form of the WZ term with this subgroup being manifest. We then show that a recently proposed expression for the four-derivative part of the effective action in N=4 USp(4) harmonic superspace yields the WZ term with manifest SO(5) R-symmetry subgroup. The N=2 SU(2) harmonic superspace form of the effective action produces the WZ term with manifest SO(4) x SO(2). We argue that there is no four-dimensional form of the WZ term with manifest SU(3) R-symmetry, which is relevant for N=1 and N=3 superspace formulations of the effective action.Comment: 26 pages; minor corrections and improvement

Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in Physics". Dubna, Russia, 28 July - 2 August, 199

Vapor pressure and evaporation rate of certain heat-resistant compounds in a vacuum at high temperatures

The vapor pressure and evaporation rate of borides of titanium, zirconium, and chrome; and of strontium and carbides of titanium, zirconium, and chrome, molybdenum silicide; and nitrides of titanium, niobium, and tantalum in a vacuum were studied. It is concluded that all subject compounds evaporate by molecular structures except AlB sub 12' which dissociates, losing the aluminum