International Journal of Theoretical Physics, Vol. 40, No. 9, September 2001 ( c  2001) Gauged Nonlinear Sigma Model in Light-Front Frame: Hamiltonian and BRST Formulations Usha Kulshreshtha 1,2 Received July 27, 2000 A gauged nonlinear sigma model in one-space one-time dimension is considered in the light-front frame. The theory is seen to possess a local vector gauge symmetry. The light-front Hamiltonian and BRST formulations of this theory are investigated under some specific light-cone gauges. 1. INTRODUCTION The O (N) nonlinear sigma models (NLSM) in one-space one-time ((1 + 1)−) dimension (Callen et al., 1969; Candelas et al., 1985; Coleman et al., 1969; Henneaux and Mezincescu, 1985; Kulshreshtha et al., 1993a; Maharana, 1983a,b; Mitra and Rajaraman, 1990a,b; Ruehl, 1991a,b, 1993, 1995, 1996; Zamolodchikov and Zamolodchikov, 1979), where the field sigma is a real N-component field, provide a laboratory for the various nonperturbative techniques for example, 1/N- expansion (Ruehl, 1991a,b, 1993, 1995, 1996), operator product expansion, and the low energy theorems (Callen et al., 1969; Coleman et al., 1969). These models are characterized by features like the renormalization and asymptotic freedom com- mon to that of quantum chromodynamics, and they exhibit a nonperturbative par- ticle spectrum, have no intrinsic scale parameter, possess the topological charges, and are very crucial in the context of conformal (Ruehl, 1991a,b, 1993, 1995, 1996) and string-field theories (Candelas et al., 1985; Henneaux and Mezincescu, 1985), where they appear in the classical limit (Callen et al., 1969; Coleman et al., 1969). The Hamiltonian formulation of the gauge-non-invariant (GNI), O (N)-NLSM in (1 + 1)-dimension, has been studied in Maharana (1983a) and its two gauge- invariant (GI) versions have been constructed in Kulshreshtha et al. (1993a), where the Hamiltonian (Dirac, 1950, 1964) and Becchi–Rouet–Stora–Tyutini (BRST) (Becchi et al., 1974; Henneaux and Teitelboim, 1992; Kulshreshtha, 1998; 1 Fachbereich Physik der Universitaet Kaiserslautern, D-67653 Kaiserslautern, Germany. 2 Present address: Department of Physics, University of Delhi, Delhi 110007, India; e-mail: usha@ physics.du.ac.in. 1561 0020-7748/01/0900-1561$19.50/0 C  2001 Plenum Publishing Corporation