https://doi.org/10.1140/epjc/s10052-012-2188-6
Regular Article - Theoretical Physics
Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle
1
Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi, 221 005, U.P., India
2
DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India
* e-mail: malik@bhu.ac.in
Received:
27
June
2012
Revised:
25
September
2012
Published online:
27
October
2012
We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1,2)-dimensional supermanifold parameterized by an even (bosonic) variable (τ) and a pair of odd (fermionic) variables θ and 
(with 
, 
) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-)BRST invariant Curci–Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2012
