We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what… (More)

An explicit parameterization is given for the density matrices for n-state systems. The geometry of the space of pure and mixed states and the entropy of the n-state system is discussed. Geometric… (More)

We study the apparition of event horizons in accelerated expanding cosmologies. We give a graphical and analytical representation of the horizons using proper distances to coordinate the events. Our… (More)

We explain how structures related to octonions are ubiquitous in M theory. All the exceptional Lie groups, and the projective Cayley line and plane appear in M -theory. Exceptional G2-holonomy… (More)

A huge family of solvable potentials can be generated by systematically exploiting the factorization (Darboux) method. Staarting from the free case, a large class of the known solvable families is… (More)

This is a pedagogical exposition of holonomy groups intended for physicists. After some pertinent definitions, we focus on special holonomy manifolds, two per division algebras, and comment upon… (More)

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X = G/H , which can be considered as the phase spaces of… (More)

After a brief review of string and M -Theory we point out some deficiencies. Partly to cure them, we present several arguments for “F -Theory”, enlarging spacetime to (2, 10) signature, following the… (More)

This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the 1 + 1 + 16 = 18 families of finite… (More)