This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

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This volume contains a collection of review articles that are extended versions of invited lectures given at the First Pamporovo Winter Workshop on Cooperative Phe­ nomena in Condensed Matter held in villa "Orlitza" (7th-15th March 1998, Pamporovo Ski Resort, Bulgaria). Selected research works reported at the Workshop have been published in the Journal of Physical Studies - a new International Journal for research papers in experimental and theoretical physics (Lviv University, Lviv, Ukraine). These reviews are supposed to be status reports and present new insights gained from the rapidly developing research of outstanding problems in condensed matter physics such as structural properties and phase transitions in fullerene crystals, super­ conductivity ofstrongly interacting electrons in copper oxides, spin polarized Fermi liq­ uids, chaotic vortex filaments in superfluid turbulent Helium-II, desorption induced by electronic transitions in ionic compounds, fluctuation phenomena in superconductors, and quantum critical phenomena in low dimensional magnets and quantum liquids. We have set the material according to the alphabetic order of authors' names although the high temperature superconductivity seems to be the hard kernel in condensed matter physics. The authors have taken care to present the recent advances in their research in a form which is readable and useful not only to experts in the respective field, but also to young scientists. That is why the lectures include a comprehensive introduction to the matter and also an extended discussion of methodical details.