International Journal of Theoretical Physics, Vol. 38, No. 7, 1999 Path-Integral and BRST Quantization in a Pure Supersymmetric Anyon Model E. C. Manavella, 1 C. E. Repetto, 1,2 and O. P. Zandron 1,2 Received November 13, 1998 The constraint structure of a pure supersymmetric anyon model with U(1) gauge symmetry is analyzed in the framework of the symplectic Faddeev±Jackiw formalism. Then the path-integral method is used to develop the perturbative formalism. The Feynman rules and the diagrammatics are given. Finally, the results are compared to those obtained by means of the BRST formalism. 1. INTRODUCTION Anyonic excitations can be analyzed from different theoretical approaches (see, for instance, refs. 1±14), but a natural way to treat fractional spin and statistics is by means of supersymmetric anyon models. In the framework of gauge theories, an interesting supersymmetric for- mulation of pure anyon theories is presented in ref. 13. Starting from the standard formalism of pure anyon theories in terms of the U(1) statistical Chern±Simons (CS) field, a minimal supersymmetric model with fractional spin and statistics is constructed. This is done by direct generalization of the nonsupersymmetric case. The first important result is that the fields of spin s are connected with the fields of spin s 1 1 ± 2 by means of the supersymmetry. When the particle content and the interactions of the model are explored, an anyon±anyon interaction required by supersymmetry naturally appears. So the main conclusion is that in this type of model the interaction among anyons is a direct requirement of supersymmetry. This fact can be seen from a general point of view by defining a minimal coupling among a suitably conserved current superfield and a gauge spinor superfield. There are several reasons and advantages in considering anyon theories in the supersymmetry frame- 1 Facultad de Ciencias Exactas, IngenierõÂa y Agrimensura de la UNR, 2000 Rosario, Argentina. 2 Miembros del Consejo Nacional de Investigaciones CientõÂficas y TeÂcnicas-Argentina. 1837 0020-7748/99/0700-183 7$16.00/0 q 1999 Plenum Publishing Corporation