Wightman function for a massive scalar field with a perfectly reflecting boundary

Abstract This paper presents a rigorous yet accessible derivation of the two-point Wightman function for a massive scalar field in Minkowski spacetime in the presence of a perfectly reflecting boundary. The derivation synthesizes two established theoretical tools: the integral representation of the Wightman function for a massive field in unbounded space and the method of images for imposing boundary conditions. We first review the foundational principles of both methods and then systematically combine them to obtain a precise analytical expression for the Wightman function in the bounded geometry. The resulting expression is thoroughly analyzed, and its validity is confirmed by examining its behavior in various physical limits, including the massless limit, the large-distance limit, and the satisfaction of the boundary condition itself. We further discuss the unique physical effects introduced by the field’s mass, particularly the exponential shielding of boundary effects beyond the Compton wavelength. To demonstrate the practical utility of our result, we apply it to calculate the local Casimir energy density near the boundary, explicitly showing the mass-induced suppression. The derived function serves as a fundamental tool for investigating quantum vacuum phenomena in constrained geometries, such as the Casimir effect, entanglement harvesting, and atomic decoherence for physical systems involving massive fields or quasiparticles.