In the framework of the augmented superfield formalism, the local, covariant, continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry transformations are derived for a (0 + 1)-dimensional free scalar relativistic particle that provides a prototype physical example for the more general reparametrization invariant string-and gravitational theories. The trajectory (i.e. the world-line) of the free particle, parametrized by a monotonically increasing evolution parameter τ , is embedded in a D-dimensional flat Minkowski target manifold. This one-dimensional system is considered on a (1 + 2)-dimensional supermanifold parametrized by an even element τ and a couple of odd elements (θ andθ) of a Grassmannian algebra. The horizontality condition and the invariance of the conserved (super)charges on the (super)manifolds play very crucial roles in the above derivations of the nilpotent symmetries. The geometrical interpretations for the nilpotent (anti-)BRST charges are provided in the framework of augmented superfield approach.Keywords: Augmented superfield formalism; (anti-)BRST symmetries; free scalar relativistic particle; horizontality condition; invariance of (super)charges on (super)manifolds PACS numbers: 11.30.Ph; 02.20.+b * E-mail address: malik@boson.bose.res.in
IntroductionThe principle of local gauge invariance, present at the heart of all interacting 1-form gauge theories, provides a precise theoretical description of the three (out of four) fundamental interactions of nature. The crucial interaction term for these interacting theories arises due to the coupling of the 1-form gauge fields to the conserved matter currents so that the local gauge invariance could be maintained. In other words, the requirement of the local gauge invariance (which is more general than its global counterpart) enforces a theory to possess an interaction term (see, e.g., [1]). One of the most attractive approaches to covariantly quantize such kind of gauge theories is the Becchi-Rouet-Stora-Tyutin (BRST) formalism where the unitarity and "quantum" gauge (i.e. BRST) invariance are respected together at any arbitrary order of the perturbation theory (see, e.g., [2]). The BRST formalism is indispensable in the context of modern developments in topological field theories, topological string theories, supersymmetric gauge theories, reparametrization invariant theories (that include D-branes and M-theories), etc., (see, e.g., [3][4][5] and references therein for details).We shall be concentrating, in our present investigation, only on the geometrical aspects of the BRST formalism in the framework of augmented superfield formulation because such a study is expected to shed some light on the abstract mathematical structures behind the BRST formalism in a more intuitive and illuminating fashion. The usual superfield approach [6][7][8][9][10][11][12][13] to the BRST scheme provides the geometrical origin and interpretation for the conserved (Q (a)b = 0), nilpotent (Q for only the gauge field and (anti-)ghost fi...