Finite axionic electrodynamics from a new non-commutative approach

Using the gauge-invariant but path-dependent variable formalism, we compute the static quantum potential for non-commutative axionic electrodynamics (or axionic electrodynamics in the presence of a minimal length). Accordingly, we obtain an ultraviolet finite static potential that is the sum of a Yukawa-type potential and a linear potential, leading to the confinement of static charges. Interestingly, it should be noted that this calculation involves no θ expansion at all. The present result manifests the key role played by the new quantum of length in our analysis.