Eur. Phys. J. C (2006) 48: 825-834
https://doi.org/10.1140/epjc/s10052-006-0006-8

Theoretical Physics

Augmented superfield approach to unique nilpotent symmetries for complex scalar fields in QED

¹ Block-JD, Sector-III, S.N. Bose National Centre for Basic Sciences, Salt Lake, Calcutta, 700 098, India
² Centre of Advanced Studies, Physics Department, Banaras Hindu University, Varanasi, 221 005, India

^* e-mail: malik@bhu.ac.in

Received: 15 April 2006
Revised: 9 June 2006
Published online: 24 October 2006

Abstract

The derivation of the exact and unique nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of the superfield approach to the BRST formalism. These nilpotent symmetry transformations are deduced for the four (3+1)-dimensional (4D) complex scalar fields, coupled to the U(1) gauge field, in the framework of an augmented superfield formalism. This interacting gauge theory (i.e. QED) is considered on a six (4,2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. In addition to the horizontality condition (that is responsible for the derivation of the exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a new restriction on the supermanifold, owing its origin to the (super) covariant derivatives, has been invoked for the derivation of the exact nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above nilpotent symmetries are discussed, too.