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A path-integral quantization is presented for the chiral Schwinger model on a Riemann surface. Gauge invariance is maintained by integrating over all gauge potentials without the usual gauge fixing. All local degrees of freedom of the gauge field are suppressed after the integration of the anomalous effective action over a gauge orbit. The resulting theory is a topological one for the surviving global gauge excitations. The general implications for consistent quantization of chiral gauge theories are also discussed.

A general concept of holonomy scattering is defined. It applies, among other things, to imply a nontrivial (generally, inelastic) scattering amplitude for the scattering of pure flux tubes off one another, when these fluxes are non-Abelian and do not commute. The amplitudes for such processes, as well as the original Aharonov-Bohm cross section, are calculated directly from an expression for the propagator with a definite winding number.

The present time variation of coupling constants in superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of internal space. If the potential is almost flat, as in perturbation theory to all orders, the value of G-italic-dot/G for Newton's gravitational constant is calculable and estimated to be -1 x 10/sup -11//sup +- //sup 1/ yr/sup -1/. If the potential has a minimum with finite curvature due to unknown nonperturbative effects, G-italic-dot/G will become unobservably small. Improvement of the measurement of G-italic-dot/G would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.

Because of complicated topology of the configuration space for indistinguishable particles in two dimensions, Feynman's path-integral formulation allows exotic statistics. All possible quantum statistics in two-space are characterized by an angle parameter $\ensuremath{\theta}$ which interpolates between bosons and fermions. The current formalisms in terms of topological action of multivalued wave functions can be derived in a model-independent way.

We formulate a geometrical theory of self-dual scalar fields in two dimensions with a local Lorentz-invariant action. Path-integral quantization is used to derive chiral Bosonization by demonstrating equivalence of correlation functions of currents and energy-momentum tensors in our theory with those for Weyl fermions.

We argue that the ..beta.. function for the statistics parameter in (2+1)-dimensional electrodynamics is zero to all orders in perturbation theory beyond one loop. We show that there can be finite radiative corrections from massless charged scalar fields.