A New Proposal for Matrix Theory

We give a detailed exposition of our recent proposal for Matrix Theory. Starting with the pedagogical case of bosonic matrix theory we identify a matrix Lagrangian whose large N limit coincides with the spacetime Lagrangian of an open and closed bosonic string theory. We describe the appearance of spacetime and of the basic elements of spacetime geometry in our framework. We identify the symmetry algebra governing the matrix Lagrangian at finite N and illustrate the phenomenon of matrix Dbrane democracy. The supersymmetric matrix Lagrangian is a nontrivial extension of the bosonic theory giving rise in the large N limit to the spacetime Lagrangians of supersymmetric open and closed string theories with Dbranes. We give a matrix path integral prescription for the Hartle-Hawking wavefunction of the Universe derived from Matrix Theory