Gauge Invariance Approach to Acoustic Fields

Description

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. Front Matter ....Pages i-xvii Introduction (Woon Siong Gan)....Pages 1-2 History of Gauge Theory (Woon Siong Gan)....Pages 3-13 Coordinate Systems as the Framework of Equations (Woon Siong Gan)....Pages 15-20 Gauge Fields (Woon Siong Gan)....Pages 21-26 Covariant Derivative in Gauge Theory (Woon Siong Gan)....Pages 27-30 Lie Groups (Woon Siong Gan)....Pages 31-41 Global Gauge Invariance (Woon Siong Gan)....Pages 43-45 Local Gauge Invariance (Woon Siong Gan)....Pages 47-50 Gauge Fixing (Woon Siong Gan)....Pages 51-53 Noether’s Theorem (Woon Siong Gan)....Pages 55-58 Spontaneous Symmetry Breaking and Phonon as the Goldstone Mode (Woon Siong Gan)....Pages 59-62 Time Reversal Acoustics and Superresolution (Woon Siong Gan)....Pages 63-93 Negative Refraction, Acoustical Metamaterials and Acoustical Cloaking (Woon Siong Gan)....Pages 95-124 New Acoustics Based on Metamaterials (Woon Siong Gan)....Pages 125-169