Abstract The neutrino, its mysterious nature and its role in the understanding of structure of matter and its relationship to physics at large scale has been of profound recent interest. In the standard model of electroweak gauge theory and its minimal extension, the neutrino occupies a central place as a building block of matter. The phenomenon of neutrino traversing and interacting with fields (matter and electromagnetic) in a medium has been under intense study for several years as neutrino dispersion in the framework of minimal standard model. Such a study is known to yield matter and magnetic field induced neutrino oscillations which possess far reaching implications for both terrestrial as well as extraterrestrial physics. For its applicability to and interest in solar neutrino problem, cosmology and other issues of astroparticle physics, we study, therefore, the neutrino dispersion through hot and dense medium in two model extensions of the standard model: one based on nonzero neutrino mass admitting the possibility of large enough magnetic moment for the neutrino yielding helicityflip effects which result in spinflavour oscillations. The other yielding neutrino oscillations within the context of the minimal extension of the standard model based on supersymmetry, the latter presumably being of more recent phenomenological interest. We then present a simple study of an effect analogus to the classical Faraday effect for a dispersing neutrino de Broglie wave. This study leads to some understanding of the nature of neutrino in analogy with classical phenomenon and provides a natural, generic and consistent choice of the oscillations parameters corresponding to different oscillations scenarios. In the study of v refraction in a minimal supersymmetric standard model with explicitly broken Rparity at finite temperature and density, it is found that sfermions coupled with fermions give rise to chirality conserving as well as chirality violating corrections to neutrino transitions. Some of the implications of these results to the solar neutrino problem, supernovae and early universe are discussed and compared with earlier works. We also study the issue of leptonflavour violating Zo decays in minimal supersymmetric standard model. This result in the vacuum serves as an input in the framework of the FTD theory yielding further results of interest to astrophysics and cosmology. We have explicitly demonstrated that in this model present limits from lowenergy processes can in principle accommodate these decays to values near the experimental bounds.
