We study the hydrostatic equilibrium of multi-Weyl semimetals, a class of systems with Weyl-like quasi-particles but anisotropic dispersion relation ω2 ∼ \( {k}_{\parallel}^2 \) + \( {k}_{\perp}^{2n} \) , with n a possitive integer. A characteristic feature of multi-Weyl systems is the lack of Lorentz invariance, instead, they possess the reduced spacetime symmetry (SO(1, 1) × SO(2)) ⋉ ℝ4. In this work we propose a covariant formulation for the low energy theory, allowing for a minimal coupling of the fermion field to external geometric background and U(1) gauge field. The non-Lorentzian structure of the field theory demands introducing an Aristotelian spacetime analogous to the so-called stringy Newton-Cartan geometry [Andringa et al. (2012) arXiv:1206.5176]. Our proposal allows for a systematic study of the hydrostatic properties via the derivation of the partition function of the system. In addition to multi-Weyl models, our formulation can be applied to systems with similar spacetime symmetry groups, such as Bjorken flow.
