Quaternions and M(atrix) theory in spaces with boundaries
Abstract
Description
A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The construction causes the elements of matrices to be equivalent to real numbers or quaternions and the symmetry U(2N) of the original model is reduced to O(2N) or USp(2N)=U(N,H). We also show that membranes end on the boundary of the spacetime correctly in this construction.
plain LaTeX, 15 pages, 1st revision: references, school info and notes added (real matrix case, Mobius membranes and so on...) 2nd revision: notes on originators of ideas
plain LaTeX, 15 pages, 1st revision: references, school info and notes added (real matrix case, Mobius membranes and so on...) 2nd revision: notes on originators of ideas