Dimitra Karabali

Certain nonperturbative phenomena appearing in two specific (2 + 1) dimensional models are studied.

The phenomenon of fractional spin and exotic statistics in (2 + 1) dimensions is analyzed in the context of a specific field theoretic model, namely the (2 + 1) dimensional 0(3) nonlinear sigma model, with a topological action, the Hopf term. It admits solitons, which acquire fractional spin, due to the topological term in the action. Canonical quantization methods are used to determine the fractional spin in terms of the topological charge Q of the solitons and the coefficient $\theta$ of the Hopf term. A semiclassical quantization in terms of collective coordinates in the Q = 1 sector is also carried out. The current algebra of the model is constructed and it is argued that the coefficient $\theta$ can be understood as a parameter labelling different representations of the current algebra.

The nonperturbative phenomenon of dynamical symmetry breaking is analyzed in the context of the (2 + 1) dimensional massless quantum electrodynamics with N species of fermions, treated in a 1/N expansion. The model exhibits a chiral symmetry which is spontaneously broken by dynamically generated fermion masses. The Dyson-Schwinger equations for the model are studied and it is shown that there exist symmetry breaking solutions. Their stability is investigated by evaluating the effective potential. A large hierarchy between the dynamical fermion mass and the fundamental scale of the theory $\alpha\equiv$ e$\sp2$N, where e is the gauge coupling constant, is found. The behavior of the dynamical fermion mass is such that it explicitly breaks an approximate scale invariance that the underlying theory possesses at momentum scales small compared to $\alpha$. The possibility of dynamical, gauge invariant masses for the photon and fermions, that violate parity and time-reversal invariance is also studied. It is shown that the symmetry breaking pattern is such that parity and time-reversal are not spontaneously broken.