  Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of a
scale invariant theory which does not possess conformal symmetry -- the special
conformal transformation(SCT) explicitly breaks the gauge invariance of the
theory. In this work, we construct a non-local gauge-invariant extension of the
SCT, which is compatible with the BRST formalism and defines a new symmetry of
the physical Hilbert space of the Maxwell theory for any dimension $d\geqslant
3$. We prove the invariance of the Maxwell theory in $d\geqslant 3$ by
explicitly showing that the gauge-invariant two-point correlation functions,
the action, and the classical equation of motion are unchanged under such a
transformation.
