A conducting surface in Lee–Wick electrodynamics

Abstract

Lee-Wick electrodynamics in the vicinity of a conducting plate is investigated. The propagator for the gauge field is calculated and the interaction between the plate and a point-like electric charge is computed. The boundary condition imposed on the vector field is taken to be the one that makes, on the plate, the normal component of the dual field strength to the plate vanish. It is shown that the image method is not valid in Lee-Wick electrodynamics.

Casimir effect in Podolsky electrodynamics: A functional approach

“…16, in a perfect conducting plane, the Lorentz force parallel to the conducting surface is zero. The Lorentz force in the Podolsky electrodynamics is the same as the one found in the Maxwell electrodynamics.…”

“…16, the interaction energy between the plane and a point-like charge can be obtained from the formula…”

“…The result shows that the image method is no longer valid in Podolsky electrodynamics. 16 In special, we considered the situation where ma >> 1.…”

“…As a result, their expression for this new Lagrangian exhibits a free parameter that can be identified as the inverse of a mass, the Podolsky's mass m. The modification gives the correct expression for the self-force of charged particles, shown by Frenkel and interesting effects produced by the presence of external sources. [13][14][15][16] The fact that the theory is finite in a classic point of view (the self-energy of the electron charge) will reflect in the same way in a quantum description. The theory have the quality of control the UV divergences in a sense closely related to the Pauli-Villars-Rayski regularization scheme.…”

“…Using (16), (18), (19) and (20), discarding the energy of the free field (without the presence of the conducting plate and the charge), the self energy of the conducting plate and the self energy of the particle, we can write the interacting energy between the plane and the particle…”