The Relative Trace Formula in Electromagnetic Scattering

Explore electromagnetic scattering through a lecture on the relative trace formula. Delve into the effects of perfectly conducting obstacles on electromagnetic fields, examining the comparison of scenarios using boundary layer theory. Understand the challenges in obtaining the trace formula due to Maxwell's equations' divergence-free condition without charge. Investigate necessary spaces for the Lipschitz case and discover the relationship between the xi function and scattering matrices for 1-forms. Cover topics including open bounded domains, obstacles, Maxwell's equations, Maxwell spaces, ellipse domains, layer potentials, single layer operators, the Casimir effect, boundary layer operators, and the Maxwell single operator. Gain insights into this complex subject through a comprehensive outline, literature review, and proof discussion.