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Abstract
A significant difference between classical and quantum systems involving interactions is generally accepted. Classical systems are characterized by potentials for interactions with physical parameters like mass and charge involving constitutive equations such as stress, strain, electric potentials and waves, and elastic, gaseous, and electromagnetic fields. Without explicit wave motion, classical equations of motion also involve phase because time is involved with all motion. When waves are present, such as sound and electromagnetic waves, phase is definitively involved in determining interactions, leading to modulation and ultimately to parametric amplification. The existence of de Broglie waves for all matter mandates a wave representation. Thus, quantum mechanics becomes the most important addition to all interactions. However, as with classical systems, we need to recognize that all parameters, including strain, thermal expansion, dielectric constant, and magnetization in electric and magnetic fields are also expressed in terms of constitutive relationships constructed on positive definite average quantities in the absence of phase. These quantities are typically characterized by the catch-all phrase random phase approximation (RPA) introduced by Bohm and Pines to allow interactions to be represented by parameters.
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CHAPTER 1
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