论文标题
探索自适应扰动方法的自发对称性破裂的起源
Explore the Origin of Spontaneous Symmetry Breaking from Adaptive Perturbation Method
论文作者
论文摘要
当物理系统的基本定律对称时,自发对称性破坏发生,但是系统选择的真空状态不是。与其他更复杂的理论相比,(3+1)d $ ϕ^4 $理论相对简单,这是研究非平凡真空的起源的良好起点。自适应扰动方法是一种用于处理强耦合系统的技术。强相关系统的研究对于测试全息图很有用。它在强烈耦合的QM方面已经成功,并且正在推广到标量场理论,以分析强耦合方案中的系统。不受干扰的汉密尔顿人不会与通常的数字运营商通勤。但是,量化标量场在作用在真空上时接收平面波的膨胀。在量化标量场理论的同时,可以将场扩展到平面波模式中,从而使计算更加易于处理。但是,洛伦兹对称性描述了在某些时空变换下如何保持物理定律如何保持相同的对称性,在这种方法中可能不会表现出来。提出的Feynman图表的优雅重新召集旨在恢复计算中的Lorentz对称性。使用此方法获得的结果与数值解相结合的特定值$λ= 1、2、4、8、16 $。最后,我们找到了量子琐事的证据,其中该理论在紫外线中需要$λ= 0 $。该结果意味着仅$ ϕ^4 $理论就不会经历SSB,并且$ \ langle ϕ \ rangle = 0 $ phops在RG-Flow下受到高斯固定点的边界的保护。
Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $ϕ^4$ theory is relatively simple compared to other more complex theories, making it a good starting point for investigating the origin of non-trivial vacua. The adaptive perturbation method is a technique used to handle strongly coupled systems. The study of strongly correlated systems is useful in testing holography. It has been successful in strongly coupled QM and is being generalized to scalar field theory to analyze the system in the strong-coupling regime. The unperturbed Hamiltonian does not commute with the usual number operator. However, the quantized scalar field admits a plane-wave expansion when acting on the vacuum. While quantizing the scalar field theory, the field can be expanded into plane-wave modes, making the calculations more tractable. However, the Lorentz symmetry, which describes how physical laws remain the same under certain spacetime transformations, might not be manifest in this approach. The proposed elegant resummation of Feynman diagrams aims to restore the Lorentz symmetry in the calculations. The results obtained using this method are compared with numerical solutions for specific values of the coupling constant $λ= 1, 2, 4, 8, 16$. Finally, we find evidence for quantum triviality, where self-consistency of the theory in the UV requires $λ= 0$. This result implies that the $ϕ^4$ theory alone does not experience SSB, and the $\langle ϕ\rangle = 0$ phase is protected under the RG-flow by a boundary of Gaussian fixed-points.