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Advances in High Energy Physics
Volume 2016 (2016), Article ID 6367545, 11 pages
Research Article

Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields

1Physics Department, Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh 221 005, India
2DST Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221 005, India

Received 28 December 2015; Accepted 26 April 2016

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2016 T. Bhanja et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates (with ) and a pair of Grassmannian variables () which satisfy the standard relationships: and  . Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields.