Gauge Theory Formulation of Acoustical Imaging
There are many similarities between electromagnetic waves and sound waves. Maxwell’s equation is the oldest gauge theory. Three main aspects of gauge theory are considered: (1) symmetries, (2) gauge invariance, (3) covariant form of the wave equation. Two of my discoveries mentioned in my earlier papers are revisited here: (1) symmetries of velocity field and stress field in the acoustic equations of motion, (2) a new stress field equation. Higher order Christoffel equation and higher order stress field equation are derived. The latter will form the basis of a new form of imaging the nonlinear elasticity imaging. The advantages of the application of gauge theory to acoustical imaging are mentioned.
KeywordsLagrangian Symmetries Gauge invariance Stress field Elasticity Action principle Stiffness Vector potential Covariant form Wave equation
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