The Field in the Presence of Conductors

Walter Thirring
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Walter Thirring: University of Vienna, Institute for Theoretical Physics

Chapter 3 in A Course in Mathematical Physics 2, 1978, pp 102-154 from Springer

Abstract: Abstract Realistic situations do not very closely resemble the idealization discussed in the preceding chapter, where the charge distribution is prescribed. The field in turn influences the motion of the charges, so it would be more correct to analyze the coupled system. For a point-particle the analysis is subject to the difficulties encountered in §2.4. Moreover, the charge-carriers in matter, electrons and atomic nuclei, are governed by the laws of quantum mechanics, and their motion is a very complicated many-body problem. Every phenom- enological description of matter is of necessity either highly idealized or else so general as to contain little information. Notwithstanding that objection, in order to formulate the ideas of this chapter mathematically, we shall single out one of the many models for a superconductor, which can be cast in a simple mathematical form. It is good enough for our purposes, as we shall always consider an extreme case in the examples, for which the chargecarriers in matter are numerous and move about freely. By responding instantaneously to any applied field, they cause the net field within the material to disappear entirely. Later, when we treat the gravitational interaction, this model wi11 serve as our prototype of charged matter.

Keywords: Saddle Point; Green Function; Integration Contour; Resonant Cavity; Axial Magnetic Field (search for similar items in EconPapers)
Date: 1978
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DOI: 10.1007/978-1-4419-8762-4_3

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