2026/04/30 by Anonymous, Claudio Bórquez, Byron Droguett
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-th
paper · pdf · doi:10.1103/tkzq-5b8j
openalex publication_date 2026/07/08 · openalex created_date 2026/07/09 · openalex updated_date 2026/07/30
We present a theoretical analysis of the one-loop effective potential of a self-interacting real scalar field in the presence of two parallel conducting plates with geometric roughness. The analysis is restricted to the adiabatic regime of smoothly varying surface deformations, where derivative contributions to the surface profile can be neglected. Using Wentzel-Kramers-Brillouin methods to evaluate the spectral density of the modified Laplace-Beltrami operator, together with contour integration within a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>ζ</a:mi> </a:mrow> </a:math> -function regularization scheme, we derive analytical expressions for the quantum corrections to the effective potential induced by perturbative boundary roughness and finite temperature. Furthermore, within this regime, we compute explicit contributions to the Casimir energy and to the topological mass generation associated with the geometry.