Constitutive relations in inhomogeneous systems and the particle-field conundrum

Recently a general framework has been proposed for constitutive relations. This theoretical approach attempted to represent constitutive relations as spatiotemporal differential operators acting on the physically observable fields. The general statement is sufficiently broad to embrace linear and nonlinear systems, and dispersive as well as inhomogeneous systems. The present study investigates specific examples related to polarizable and chiral media. It was immediately realized that prior to working out the examples, we have to better understand the relation of the kinematics of particles to field concepts. Throughout, the Minkowski space notation and related relativistic ideas are exploited for simpler notation and deeper understanding.