7 - Gauge Field Theory of Dislocations and Defects

Summary

One of the prominent advantages of the gauge formalism as a field theory is its sophisticated mathematical structure, being based on analytical mechanics. Everything about the system dynamics that we need can be derived by rote out of a Lagrangian density of the system, which itself can be determined uniquely based on the prescribed symmetry underlying in the physical phenomenon we want to describe. In our case, we can find how the dislocation and defect fields should be incorporated into the continuum theory of elasticity, with direct correspondences to the differential geometrical (DG) counterparts introduced in Chapter 6. Also the formalism can provide us with a bridge between the DG pictures and the method of quantum field theory (QFT) discussed in Chapter 8 via the Lagrangian density.