Field-theory spin and momentum in water waves

Spin is a fundamental yet nontrivial intrinsic angular-momentum property of quantum particles or fields, which appears within relativistic field theory. The spin density in wave fields is described by the theoretical Belinfante-Rosenfeld construction based on the difference between the canonical and kinetic momentum densities. These quantities are usually considered as abstract and non-observable per se. Here, we demonstrate, both theoretically and experimentally, that the Belinfante-Rosenfeld construction naturally arises in gravity (water surface) waves. There, the canonical momentum is associated with the generalized Stokes-drift phenomenon, while the spin is generated by subwavelength circular motion of water particles. Thus, we directly observe these fundamental field-theory properties as microscopic mechanical properties of a classical wave system. Our findings shed light onto the nature of spin and momentum in wave fields, demonstrate the universality of relativistic field-theory concepts, and offer a new platform for their studies.