We study at the classical and quantum mechanical level the time-dependent
Yang-Mills theory that one obtains via the generalisation of discrete
light-cone quantisation to singular homogeneous plane waves. The non-Abelian
nature of this theory is known to be important for physics near the
singularity, at least as far as the number of degrees of freedom is concerned.
We will show that the quartic interaction is always subleading as one
approaches the singularity and that close enough to t=0 the evolution is driven
by the diverging tachyonic mass term. The evolution towards asymptotically flat
space-time also reveals some surprising features.Comment: 29 pages, 8 eps figures, v2: minor changes, references added: v3
small typographical changes
We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann-versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in favour of Brinkmann variables), and (2) the regularisation of the quantum dynamics for a certain class of singular plane waves (discussing the benefits and limitations of regularisations of the plane-wave metric itself).
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