  Elastic angular momentum is an emerging field, with some controversies on the
correct field-theory expressions and the decomposition of longitudinal and
transverse components. Motivated by the recent two papers [Phys.Rev.Lett. 128,
064301(2022), Phys.Rev.Lett. 129, 204303(2022)] on this issue, we
systematically analyze by Noether's theorem the canonical and Belinfante
energy-momentem and angular momentum, then explain why the two familiar
expressions, together with other various conservered currents, are all correct
for elastic wave. Remarkbly, to illustrate the usefullness of different
expressions, we give an example on earthquake energy measurement with a new
energy density expression which is more advantageous in practical measurement.
Moreover, since the elastic wave is distinct from a quantum one, we suggest
that the decomposition of longitudinal and transverse components, in fact,
makes sense and can be clearly expressed by the observable displacement field.
We hope that this paper would clarify the controversies, and finally we give
prospect of future work on the Geometric Spin Hall Effect of elastic wave,
where the various expressions of conserved currents would exhibit different
applications.
