Related papers: Matrix String Theory As A Generalized Quantum Theo…

A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to…

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in…

A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…

In the 1950's Wigner and collaborators provided an explanation for the spectrum of hadronic excitations in terms of Random Matrix Theory. In the 1980's it was understood that some hadronic spectral properties were generic to systems whose…

This is a brief description of what has been accomplished and what remains to be done in the construction of a nonperturbative formulation of "The Theory Formerly Known as String". It is culled from two short talks given by the author at…

String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional…

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…

Marchesini showed that the Fokker-Planck Hamiltonian for Yang-Mills theories is the loop operator. Jevicki and Rodrigues showed that the Fokker-Planck Hamiltonian of some matrix models co\"\i ncides with temporal gauge non-critical string…

String Theory is the result of the conjunction of three conceptually independent elements: (i) the metaphysical idea of a nomological unity of the forces, (ii) the model-theoretical paradigm of Quantum Field Theory, and (iii) the conflict…

In discussing the construction of a consistent theory of quantum gravity unified with the gauge interactions we are naturally led to a string theory. We review its properties and the five consistent supersymmetric string theories in ten…

Extensions (modifications) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular, generalizations of the Stringy Uncertainty Principle are…

It is shown that the world-line can be eliminated in the matrix quantum mechanics conjectured by Banks, Fischler, Shenker and Susskind to describe the light-cone physics of M theory. The resulting matrix model has a form that suggests…

We show that the recently proposed matrix model for M theory obeys the cyclic trace assumptions underlying generalized quantum or trace dynamics. This permits a verification of supersymmetry as an operator calculation, and a calculation of…

The generalized Schrodinger equation deduced in the earlier papers is compared with conventional constructions of quantum field theory. In particular, it yields the usual Schrodinger equation of quantum field theory written without normal…

The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A…

This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…

We consider quantum-mechanical path integrals for non-linear sigma models on a circle defined by the string-inspired method of Strassler, where one considers periodic quantum fluctuations about a center-of-mass coordinate. In this approach…

A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…