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Gauge Theory Formulation of Acoustical Imaging

  • W. S. GanEmail author
Conference paper
Part of the Acoustical Imaging book series (ACIM, volume 30)

Abstract

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.

Keywords

Lagrangian Symmetries Gauge invariance Stress field Elasticity Action principle Stiffness Vector potential Covariant form Wave equation 

References

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    Landau, L.D., Lifshitz, E.M.: Theory of elasticity, 3rd edn. Pergamon Press, Oxford (1986)Google Scholar
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    Landau, L.D., Lifshitz, E.M.: Mechanics, 3rd edn. Pergamon Press, Oxford (1976)Google Scholar
  3. 3.
    Gan, W.S.: Proceedings of 15th International Congress On Sound and Vibration, 6-10 July 2008, Daejeon, Korea (2008)Google Scholar
  4. 4.
    Thurston, R.N., Shapiro, M.J.: J. Acoust. Soc. Am. 41, 1112 (1967)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Acoustical Technologies Singapore Pte LtdSingaporeSingapore

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