Matrix Quantum Mechanics and 2-D String Theory. thesis] by S. Alexandrov

By S. Alexandrov

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Example text

Thus, with each matrix model one can associate a diagrammatic expansion so that the size of matrices enters only as a prefactor for each diagram. Although this idea has not led to a large progress in QCD, it gave rise to new developments, related with matrix models, in two-dimensional quantum gravity and string theory [45, 46, 47, 48, 49]. In turn, there is still a hope to find a connection between string theory and QCD relying on matrix models [50]. Besides, recently they were applied to describe supersymmetric gauge theories [51].

Therefore, the models formulated using this technology are called matrix models. Sometimes a matrix formulation is not only a useful mathematical description of a physical system, but it also sheds light on its fundamental degrees of freedom. We will be interested mostly in application of matrix models to string theory. However, in the beginning we should explain their relation to physics, their general properties, and basic methods to solve them (for an extensive review, see [42]). This is the goal of this chapter.

Unfortunately, this reformulation has not helped much in higher dimensions. 3). ) They claim to be fundamental non-perturbative and background independent formulations of Planck scale physics. However, they are based on the ideas different from the “old” matrix models of low-dimensional string theories. Also matrix models appear in the so called spin foam approach to 3 and 4-dimensional quantum gravity [57, 58]. Similarly to the models of M–theory, they give a non-perturbative and background independent formulation of quantum gravity but do not help with calculations.

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