The (p = 2) parabose – parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p = 2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose – parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscilla...

We analyze two loop quantum corrections for pseudomoduli in O’Raifeartaigh like models. We argue that R-symmetry can be spontaneously broken at two loop in non supersymmetric vacua. We provide a basic example with this property. We discuss on phenomenological applications.

We review models of supersymmetric quantum mechanics that are important in the description of supermembranes and of Dirichlet particles, which play a role in the context of M-theory. † Invited talk given at the 30 International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, August 27 31, 1996; to appear in Nuclear Physics B (Proc. Suppl.).

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suuces to integrate a Ricatti equation to construct one-parameter families of solvabl...

We show that the spectral theory of the Dirac operator D = i∂/− σ(x)− iπ(x)γ5 in a static background (σ(x), π(x)) in 1 + 1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum mechanics, and explore its consequences. PACS numbers: 11.10.Lm, 11.15.Pg, 11.10.Kk, 71.27.+a e-mail address: [email protected] permanent address

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H(±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian H are defined along certain topologically nontrivial complex curves r(±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the ma...

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there ...

We review recent developments in the theory of supermembranes and their relation to matrix models. Invited talk given at the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2 6, 1997 (to appear in Fortschritte der Physik) and at the CERN Theory Division, December 3, 1997. 1 Supersymmetric quantum mechanics Consider the class of supersymmetric Ham...

The phenomenology and prospects for a discovery of R-parity violating Supersymmetry at HERA is analysed. Emphasis is put on the direct resonant production of squarks by electron-quark fusion and all possible subsequent decay modes of the squarks are considered. In particular, the full consequences of the mixing in the supersymmetric gaugino-higgsino sector are taken into account. A rich phenome...

Supersymmetry between bosons and fermions is modeled within PT −symmetric quantum mechanics. A non-Hermitian alternative to the Witten’s supersymmetric quantum mechanics is obtained. Work supported by the grant Nr. A 1048004 of GA AS CR. e-mail: [email protected]