Review of Matrix Theory

Abstract

Matrix theory [1] is a nonperturbative theory of fundamental processes which evolved out of the older perturbative string theory. There are two well-known formulations of string theory, one covariant and one in the so-called light cone frame [2]. Each has its advantages. In the covariant theory, relativistic invariance is manifest, a euclidean continuation exists and the analytic properties of the S matrix are apparent. This makes it relatively easy to derive properties like CPT and crossing symmetry. What is less clear is that the theory satisfies all the rules of conventional unitary quantum mechanics. In the light cone formulation [3], the theory is manifestly hamiltonian quantum mechanics, with a distinct non-relativistic flavor. There exists a space of states and operators which is completely gauge invariant and there are no ghosts or unphysical degreees of freedom. Among other things, this makes it easy to identify the spectrum of states. Matrix theory is also formulated in the light cone frame and enjoys the same advantages and disadvantages as LCF string theory. Unlike perturbative string theory, matrix theory is capable of addressing many of the nonperturbative questions raised by string theory and quantum gravity.