Superspace unitary operator in QED with Dirac and complex scalar fields: Superfield approach
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
Received: 1 September 2015
Accepted: 5 October 2015
We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of the augmented version of the superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four -dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge-invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its Hermitian conjugate. The latter operator is derived without imposing any operation of Hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.
PACS: 11.30.Pb – Supersymmetry / 03.70.+k – Theory of quantized fields / 02.40.-k – Geometry, differential geometry, and topology
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