The classical amplitude for scattering of two positive helicity and n-2 negative helicity (or the other way) gauge bosons is shown to be generated by a Wess-Zumino-Witten (WZW) model for N= 4 supersymmetric gauge theory; i.e. the current algebra of the WZW model (with central charge k= 1 ) gives a Kac-Moody algebra as the symmetry behind these amplitudes.

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point with the density of states becoming infinite for the value of the magnetic field equal to the inverse of the noncommutativity parameter.The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.

The possibility of treating boundary conditions in terms of a bilocal dynamical field is formalized in terms of a boundary action. This allows for a simple path-integral perturbation theory approach to physical effects such as radiation from a time-dependent boundary. The nature of the action which governs the dynamics of the bilocal field is investigated for a limited case (which includes the Robin boundary conditions).

We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in (2+1) dimensions, extending our previous analysis using gauge-invariant matrix variables. The vacuum wavefunction is consistent with what is expected at both high and low momentum regimes. The value of the string tension is in very good agreement with recent lattice Monte Carlo evaluations.

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