TL;DR
This paper demonstrates that gauge invariance of the effective potential in scalar electrodynamics is unaffected by the addition of a Chern-Simons term, regardless of the Maxwell term's presence.
Contribution
It provides an explicit proof that gauge invariance remains intact in Chern-Simons systems with scalar electrodynamics, independent of Maxwell term inclusion.
Findings
Gauge invariance is preserved with Chern-Simons terms.
The result is independent of Maxwell term presence.
Effective potential remains gauge invariant in these systems.
Abstract
We show explicitly that the question of gauge invariance of the effective potential in standard scalar electrodynamics remains unchanged despite the introduction of the Chern-Simons term. The result does not depend on the presence of the Maxwell term in the Chern-Simons territory.
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