Uncovering Hidden Spin of Scalar Fields with Higher-Order Derivative Lagrangian: On the Wave Spin in Drifted and Dissipative Fields

Abstract Scalar fields should have no spin angular momentum according to conventional textbook understandings in classical field theory. Yet, recent studies demonstrate the undoubted existence of wave spin endowed by acoustic and elastic longitudinal waves, which are of irrotational curl-free nature without vorticity and can be described by scalar fields. Moreover, the conventional theory cannot even answer the question of whether wave spin exists in dissipative fields, given the ubiquitous dissipation in reality. Here, to resolve the seeming paradox and answer the challenging question, we uncover the origin of wave spin in scalar fields beyond traditional formalism by clarifying that the presence of higher-order derivatives in scalar field Lagrangians can give rise to non-vanishing wave spin. For “spinless” scalar fields of only first-order derivatives, we can make the hidden wave spin emerge by revealing a latent field that leads to the original field through a time derivative, thus giving higher-order terms in Lagrangian. Based on the standard Noether theorem approach, we exemplify the wave spin for unconventional drifted acoustic fields, and even for dissipative media, in scalar fields with higher-order derivative Lagrangian. The results would prompt people to build more comprehensive and fundamental understandings of structural wave spin in classical fields.