论非相对论约化及其应用
On the subtelties of nonrelativistic reduction and applications
摘要：
讨论了将标量场理论非相对论化约为薛定谔理论的各种微妙之处和问题。与讨论运动方程或作用量之间的映射的通常方法相反，我们强调时空生成器之间的映射。使用零减少，我们显示了嵌入的共形发电机的薛定谔理论的一个复杂的标量理论在一个更高的维度。作为应用，我们揭示了流体力学中的共形对称性，并从相对论对称性得到了NR共形对称性。本文讨论了基于Horava-Lifshitz和Newton-Cartan时空的一种几何联系。
英文摘要：
Various subtleties and problems associated with nonrelativistic (NR) reduction of a scalar field theory to the Schroedinger theory are discussed. Contrary to the usual approaches that discuss the mapping among the equations of motion or the actions, we highlight the mapping among the space time generators. Using a null reduction we show the embedding of the conformal generators of the Schroedinger theory to that of a complex scalar theory in one higher dimension. As applications we reveal the conformal symmetry in hydrodynamics and the obtention of NR diffeomorphism symmetry from the relativistic one. A geometrical connection based on Horava-Lifshitz and Newton-Cartan spacetime is discussed.
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