非相对论性平方反比势、标度anomaly和复延拓
Nonrelativistic inverse square potential, scale anomaly, and complex extension
摘要：
用场论的泛函重整化方法处理非相对论量子力学中奇异平方反比势的老问题。突发接触耦合流到一个固定点或发展一个极限环取决于其二次贝塔函数的判别式。我们分析了共形和非共形阶段的不动点，并将重整化群分析自然扩展到接触耦合的复值。这种扩展的物理解释和动机是在两体碰撞中存在非弹性散射通道。通过考虑黎曼球面上的重整化群流，给出了复推广的几何描述。最后，利用玻色化，我们得到了扩展的重整化群流方程的解析解，这是我们工作的主要结果。
英文摘要：
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit cycle depending on the discriminant of its quadratic beta function. We analyze the fixed points in both conformal and non-conformal phases and perform a natural extension of the renormalization group analysis to complex values of the contact coupling. Physical interpretation and motivation for this extension is the presence of an inelastic scattering channel in two-body collisions. We present a geometric description of the complex generalization by considering renormalization group flows on the Riemann sphere. Finally, using bosonization, we find an analytical solution of the extended renormalization group flow equations, constituting the main result of our work.
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