We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking.

中文翻译：

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流体动力学的有效场论，无需升压

我们在没有增强对称性的情况下制定了流体动力学的 Schwinger-Keldysh 有效场理论。这包括经典流体动力学的时空协变公式，没有附加的守恒粒子/电荷电流与亚里士多德背景源耦合。我们发现，至一阶导数，该理论的特点是热力学状态方程和总共29个独立的输运系数，特别是3个静水压、9个非静水压非耗散和17个耗散。此外，我们研究了具有非零流体速度的各向异性平衡状态周围的线性波动谱。该分析揭示了一对声音模式，它们以不同的速度沿着流体流动并与流体流动相反，一种电荷扩散模式，以及沿和垂直于流体速度的两种不同的剪切模式。我们将这些结果呈现在一个新的流体动力学框架中，该框架是线性稳定的，而与适当的升压对称性无关。这为在有效的场论框架内同时处理洛伦兹、伽利略和 Lifshitz 流体提供了一种统一的协变稳定方法，并为未来研究非相对论性交织的对称性破坏模式奠定了基础。