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.