Canonical quantization of non-anticommutative scalar field theory

In this Letter we investigate the canonical quantization of the real scalar field theory on non-anticommutative superspace. At the classical level we derive the equation of motion and the energy–momentum tensor. Then following the standard method we perform the canonical quantization. The theory is shown to be free from the usual UV divergences. As applications we consider the computation of the cosmological constant and the Casimir force for the scalar massless field confined between parallel square plates.