The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a...

This Edited Volume is based on a workshop on Mathematical and Physical - pects of Quantum Gravity held at the Heinrich-Fabri Institute in Blaubeuren st (Germany) from July 28th to August 1, 2005. This workshop was the succ- sor of a similar workshop held at the same place in September 2003 on the issue of Mathematical and Physical Aspects of Quantum Field Theories . Both wo- shops were intended to bring together mathematicians and physicists to discuss profoundquestionswithin the non-emptyintersectionofmathematics andphysics. The basic idea of this series of workshops is to cover a broad...

The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po- sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans- lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space 2, 7J means that the mutual Pois- son bracket relations among the total angular momentum functions Mab and...