|MadSci Network: Physics|
Dear Alex, I am not sure what you mean by four "geometric" dimensions. We normally think of three "space" (or geometric) dimensions, and one time dimension. However, everything, fermions and bosons alike, can really only only described in four dimensions, as everything has a position and a momentum. Further information can be found in any text on elementary particles. My personal favorite is by Griffiths, Introduction to Elementary Particles.
Try the links in the MadSci Library for more information on Physics.