发表机构
Universidad del Valle（德瓦列大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨了有限圆柱区域内旋转标量场的Z_2对称性恢复，通过背景场方法和环求和得到空间分辨有效势，发现转变温度的旋转修正依赖于横向尺寸和有限谱结构。
AI 中文摘要
我们研究了在有限圆柱区域内进行刚性旋转的实λφ^4理论中的Z_2对称性恢复。通过Dirichlet边界条件施加有限的横向范围，导致离散的Fourier-Bessel谱和涨落传播子的显式径向依赖性。利用背景场方法，我们推导了单圈有效势，同时保留了有限几何结构诱导的空间结构。在有限温度下，旋转通过角动量依赖的热模式能量移动进入，将旋转状态与离散横向谱耦合。由此产生的重合点传播子定义了位置相关的热自能，并通过环求和纳入有效势。这产生了一个空间分辨的有效势，其结构同时依赖于背景场、温度、角速度和横向尺寸。然后我们使用其空间平均值来确定对称性恢复温度，并研究其对旋转状态和有限体积谱的依赖性。结果表明，转变温度的旋转修正保留了横向尺寸的显式依赖性，反映了有限旋转系统的谱结构，而非仅仅与光圆柱相关的因果约束。
英文摘要
We investigate $\mathbb{Z}_2$ symmetry restoration in a real $λϕ^4$ theory confined to a finite cylindrical region undergoing rigid rotation. The finite transverse extent is imposed through Dirichlet boundary conditions, resulting in a discrete Fourier-Bessel spectrum and an explicit radial dependence of the fluctuation propagator. Using the background-field method, we derive the one-loop effective potential while retaining the spatial structure induced by the finite geometry. At finite temperature, rotation modifies the thermal mode energies through angular-momentum-dependent shifts, and the coincident-point propagator generates a position-dependent thermal self-energy that is incorporated through ring resummation. We use the resulting spatially resolved effective potential to determine the symmetry-restoration temperature $T_c(Ω,R)$ and examine its dependence on the angular velocity and transverse size. The results show that the finite transverse size of the system modifies the symmetry-restoration temperature, leading to a nontrivial dependence of $T_c(Ω,R)$ on $R$. An additional scaling behavior emerges when the normalized critical temperature is expressed in terms of the boundary velocity $ΩR$: systems with different transverse sizes exhibit the same relative modification of $T_c$ when their boundary velocities are equal. This scaling persists after the inclusion of the position-dependent thermal self-energy through ring resummation, indicating that the $ΩR$ dependence of the rotational response is maintained in the interacting finite system.
Comments21 pages, 1 figure, 5 appendices. The Discussion section has been revised and expanded. The title has also been changed
