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What is fundamental - gauge fields or gauge invariance? A perspective from modeling defects in continuum mechanics

Amit Acharya (Carnegie Mellon University)

SES Medal Symposium in honor of D.J. Steigmann

Mon 10:45 - 12:15

MacMillan 115

I show how objects like gauge fields appear in the continuum mechanics of dislocation plasticity and nematic disclinations as an outcome of modeling the physical fact that finite bodies have finite energies. This obviates the need for a principle of gauge invariance to introduce the gauge fields, which postulates global symmetries of solutions of defectless theories be rendered local. In fact, to reproduce the (suitably regularized) classically accepted Volterra displacement and stress solution for the edge dislocation and that for the director and energy density field of the Frank wedge disclination, gauge invariance is necessarily violated. Part of the analysis proceeds by understanding the anatomy of the Volterra solution through a Stokes-Helmholtz resolution and then taking a limit where the latter provides flexibility to produce finite energy.