Gauge Invariance Approach to Acoustic Fields

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • Woon Siong Gan

   Pages 1-2

3. History of Gauge Theory

   • Woon Siong Gan

   Pages 3-13

4. Coordinate Systems as the Framework of Equations

   • Woon Siong Gan

   Pages 15-20

5. Gauge Fields

   • Woon Siong Gan

   Pages 21-26

6. Covariant Derivative in Gauge Theory

   • Woon Siong Gan

   Pages 27-30

7. Lie Groups

   • Woon Siong Gan

   Pages 31-41

8. Global Gauge Invariance

   • Woon Siong Gan

   Pages 43-45

9. Local Gauge Invariance

   • Woon Siong Gan

   Pages 47-50

10. Gauge Fixing

    • Woon Siong Gan

    Pages 51-53

11. Noether’s Theorem

    • Woon Siong Gan

    Pages 55-58

12. Spontaneous Symmetry Breaking and Phonon as the Goldstone Mode

    • Woon Siong Gan

    Pages 59-62

13. Time Reversal Acoustics and Superresolution

    • Woon Siong Gan

    Pages 63-93

14. Negative Refraction, Acoustical Metamaterials and Acoustical Cloaking

    • Woon Siong Gan

    Pages 95-124

15. New Acoustics Based on Metamaterials

    • Woon Siong Gan

    Pages 125-169

This book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials.
  
The book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage.   

• Covariant derivative
• Global gauge invariance
• Time reversal symmetry
• Global symmetry
• Vector potential
• Non-Abelian group symmetry
• Local gauge invariance
• Reflection Invariance
• Acoustic metamaterials
• Finite amplitude waves
• Acoustical imaging

• Acoustical Technologies Singapore Pte Ltd., Singapore, Singapore

  Woon Siong Gan

Dr. Woon Siong Gan completed his PhD at the age of 24, and is one of the founders of condensed matter physics. He was the first to introduce transport theory into condensed matter physics, and coined the term “transport theory” in 1966, during his PhD studies at the physics department of Imperial College London. Today, transport theory is the key foundation of the theoretical design of new materials and enjoys a status in condensed matter physics similar to that of Yang Mills theory in particle physics.  His PhD thesis (1969) employed a statistical mechanics approach to describe phase transition and ultrasound propagation in semiconductors in the presence of high magnetic fields and low temperatures instead of the usual method of electron-phonon interaction from many body theory. Accordingly, his thesis also played a part in the founding of condensed matter physics. 

In 2007 he introduced a gauge invariance approach to acoustics fields, a milestone in the history of gauge invariance in physics.  Recently he has also introduced curvilinear spacetime for the treatment of nonlinear acoustics; a suitable choice due to the curved paths of high-intensity acoustic fields.  

Dr. Woon Siong Gan authored the books Acoustical Imaging: Techniques and Applications for Engineers, published by John Wiley & Sons in 2012, and New Acoustics Based on Metamaterials, published by Springer in 2018.  This is his third book, Gauge Invariance Approach to Acoustics Fields, published by Springer. His current research interests are in transport theory approaches to phase transition, quantum acoustic metamaterials, and curvilinear spacetime approaches to nonlinear acoustics.

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