自旋流体动力学的正则与唯象表述
Canonical and phenomenological formulations of spin hydrodynamics
AI总结：
本文比较自旋1/2粒子相对论流体动力学的正则与唯象表述，证明通过改进能量-动量张量并利用赝规范变换可使二者等价，且熵产生正定性一致。
摘要：
本文比较了自旋为1/2粒子的相对论流体动力学的两种表述。第一种方法被称为正则方法，它使用能量-动量张量和自旋张量的表达式，这些表达式的性质源于直接应用Noether定理，由此产生一个完全反对称的自旋张量。另一种方法基于自旋张量的简化形式，在当前文献中通常被称为唯象方法。我们证明，这两种框架是等价的，即它们可以通过适当定义的赝规范变换直接联系起来，但前提是第一种框架首先要通过对能量-动量张量进行适当修改而得到改进（加入一个无散度项，而该项不能被解释为赝规范变换）。我们的分析使用了与熵产生正定性相关的论证。结果表明，对于改进后的正则框架和唯象框架，后者是等价的。
英文摘要：
Two formulations of relativistic hydrodynamics of particles with spin 1/2 are compared. The first approach, dubbed the canonical one, uses expressions for the energy-momentum and spin tensors that have properties that follow a direct application of Noether's theorem, which yields a totally antisymmetric spin tensor. The other one is based on a simplified form of the spin tensor and is commonly used in the current literature under the name of a phenomenological approach. We show that these two frameworks are equivalent, i.e., they can be directly connected by a suitably defined pseudogauge transformation, only if the first framework is initially improved by a suitable modification of the energy-momentum tensor (addition of a divergence-free term that cannot be interpreted as a pseudogauge). Our analysis uses arguments related to the positivity of entropy production. The latter turns out to be equivalent for the improved canonical and phenomenological frameworks.
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