壳层上T矩阵元和（1- $ϕ$ -I）格林函数的$U(1)\otimes BRST$对称性仅从对称性决定了阿贝尔希格斯模型的真空态：标量扇区有效势的最小化是不必要的
$U(1)\otimes BRST$ symmetry, of on-shell T-matrix elements and (1-$ϕ$-I) Green's functions, determines the vacuum state of the Abelian Higgs Model from symmetry alone: minimization of the scalar-sector effective potential is unnecessary
摘要：
弱尺度$U(1)_{Y}$阿贝尔希格斯模型（AHM）是一个复标量$ϕ= \frac{1}{\sqrt{2}}(H + i π)$和一个矢量$A_μ$的自发对称破缺规范理论。全局$U(1)_{Y}\otimes BRST$对称性出现：当认识到壳层上T矩阵元享有超越拉格朗日BRST对称性的额外$U(1)_{Y}$全局对称性时。对称性共存：$U(1)_{Y}$生成器$δ_{U(1)_Y}$与BRST生成器s和$[δ_{U(1)_Y},s]{\cal L} = 0$交换。两个塔的沃德高桥恒等式（WTI），其中包括所有的循环阶量子校正，出现：一个塔的关系之间的离壳1- $ϕ$ -I（但1- $A_μ$ -可约）格林函数;另一个塔的阿德勒零WTI的壳T矩阵元素。T矩阵的LSS定理迫使蝌蚪仅通过对称性自动消失（相当于$m^{2}_π = 0$）。我们表明，当洛伦兹规范AHM的完全对称性被强制的标量扇区有效势，真空状态的理论是指定/决定的对称性。我们使用格林函数之间的递归WTI关系来包含$\geq 1$维的算子。我们表示的完全重整化标量扇区有效势的形式，明确表明，对于小标量场值，规范无关的真空态的理论$\langle H\rangle_{renormalized} = Z^{1/2}_ϕ\langle H\rangle_{bare}$是由$U(1)_{Y}\otimes BRST$对称性单独，而不最小化的有效势。
英文摘要：
The weak-scale $U(1)_{Y}$ Abelian Higgs Model (AHM) is the spontaneous-symmetry-breaking gauge theory of a complex scalar $ϕ= \frac{1}{\sqrt{2}}(H + i π)$ and a vector $A_μ$. Global $U(1)_{Y}\otimes BRST$ symmetry emerges: when it is realized that on-shell T-matrix elements enjoy an extra $U(1)_{Y}$ global symmetry beyond the Lagragian's BRST symmetry. The symmetries co-exist: $U(1)_{Y}$ generators $δ_{U(1)_Y}$ commute with BRST generators s and $[δ_{U(1)_Y},s]{\cal L} = 0$. Two towers of Ward Takahashi identities (WTI), which include all-loop-orders quantum corrections, emerge: a tower of relations among off-shell 1-$ϕ$-I (but 1-$A_μ$-Reducible) Green's functions; another tower of Adler-zero WTI for on-shell T-matrix elements. The T-matrix's LSS theorem forces tadpoles to automatically vanish (equivalently $m^{2}_π = 0$) by symmetry alone. We show that, when the full symmetries of Lorenz gauge AHM are enforced on the scalar-sector effective potential, the vacuum state of the theory is specified/decided by symmetry alone. We use recursive WTI relations among Green's functions to include opeators of dimension $\geq 1$. We express the fully renormalized scalar-sector effective potential in a form which shows explicitly that, for small scalar field values, the gauge-independent vacuum state of the theory $\langle H\rangle_{renormalized} = Z^{1/2}_ϕ\langle H\rangle_{bare}$ is determined by $U(1)_{Y}\otimes BRST$ symmetry alone, without minimizing the effective potential.
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