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arXiv 2603.09013hep-thcond-mat.str-elmath-phmath.MP
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流体动力学作为场论到BF理论的余弦

Hydrodynamics as cospans of field theories into the BF theory

University of Hertfordshire（赫特福德大学）

Simon Jonsson, Hyungrok Kim

备注：
27 pages, no figures
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AI总结：

本文提出将流体动力学近似视为场论到BF理论的余弦，通过守恒电流的运动方程建立微观与流体动力学理论的联系。

摘要：

流体动力学基于电流守恒定律：从描述微观动力学的守恒电流出发，用流体动力学变量（密度、压力、速度等）重新参数化这些电流。这一范式最近已被扩展以纳入更高形式对称性。$p$-形式守恒电流的守恒定律可视为BF理论的运动方程，该理论将电流视为基本场。我们主张，微观理论的流体近似可视为微分格 manifold 的余弦 $X_{micro}→X_{BF}←X_{hydro}$，其中 $X_{micro}$ 和 $X_{hydro}$ 分别描述微观和流体动力学理论，而 $X_{BF}$ 描述守恒电流的BF理论。

英文摘要：

Hydrodynamics is based on conservation laws of currents: one starts from the conserved currents of the theory describing the microscopic dynamics, and provides an alternative parameterisation of these currents in terms of hydrodynamic variables (density, pressure, velocity, etc.). This paradigm has recently been extended to incorporate higher-form symmetries. The conservation law of the $p$-form conserved currents can be regarded as the equations of motion of a $BF$ theory that treats the currents as fundamental fields. We argue that the hydrodynamic approximation to a microscopic theory can be regarded as a cospan of differential graded manifolds $X_\mathrm{micro}\to X_{BF}\leftarrow X_\mathrm{hydro}$, where $X_\mathrm{micro}$ and $X_\mathrm{hydro}$ describe the microscopic and hydrodynamic theories, respectively, and $X_{BF}$ describes the $BF$ theory of conserved currents.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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