标题： 路径积分Fujikawa方法在具有$SO(2, 1)$对称性的系统中异常位力定理和状态方程的研究 显示英文标题

标题： Path-Integral Fujikawa's Approach to Anomalous Virial Theorems and Equations of State for Systems with $SO(2, 1)$ Symmetry

摘要： 我们利用藤川的路径积分方法和标度论证，推导出具有接触相互作用的非相对论二维复标量玻色场的反常状态方程。在此过程中，我们为这类系统推导出了一个反常的气体功定理。所用的方法可以轻松推广到其他的二维系统，包括费米子系统，并且适用于不同空间维度的所有系统，它们都共享经典的$SO(2,1)$Schrodinger 对称性。讨论更具形式化性质，主要目的是阐明二维多体系统中反常的结构。气体功定理和状态方程 - 压力关系中的反常修正可以被识别为 Tan 联系项。这些想法的实际应用取决于能否详细计算包含反常的藤川雅可比矩阵。本文最后还讨论了其他概念问题以及一些近期的发展。 显示英文摘要

摘要： We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical $SO(2,1)$ Schrodinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state - pressure relationship - may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.