在哈密顿形式下计算复合粒子谱及其在2味QED$_{1+1\text{d}}$中的演示
Calculating composite-particle spectra in Hamiltonian formalism and demonstration in 2-flavor QED$_{1+1\text{d}}$
AI总结：
本文在哈密顿形式下比较三种质量谱计算方法，并用DMRG研究2味Schwinger模型，识别出π、σ、η介子，发现σ介子质量轻于两倍π介子质量因而稳定，数值结果接近WKB预测的$M_σ/M_π=\sqrt{3}$。
摘要：
我们考虑三种不同的方法来计算哈密顿形式下规范理论的质量谱：（1）关联函数方案，（2）单点函数方案，以及（3）色散关系方案。第一种方法像我们在传统欧几里得蒙特卡洛模拟中那样考察空间关联函数。第二种方法利用边界效应来高效计算质量谱。第三种方法构造激发态，并在选择量子数的情况下利用色散关系拟合它们的能量。每种方法各有优缺点，我们在使用密度矩阵重整化群（DMRG）计算$m/g=0.1$和$θ=0$时2味有质量Schwinger模型的质量谱的应用中阐明了这些特性。我们注意到，小质量$m$下的多味Schwinger模型即使在玻色化之后也是一个强耦合场论，因此值得进行第一性原理数值计算。所有这些方法大体上一致，并识别出稳定粒子：π介子$π_a$（$J^{PG}=1^{-+}$）、σ介子$σ$（$J^{PG}=0^{++}$）和η介子$η$（$J^{PG}=0^{--}$）。特别是，我们发现$σ$介子的质量轻于两倍π介子质量，因此$σ$对衰变过程$σ\to ππ$是稳定的。这与使用WKB近似的解析预测一致，并且值得注意的是，我们的数值结果非常接近基于WKB的π介子与σ介子质量公式$M_σ/M_π=\sqrt{3}$。
英文摘要：
We consider three distinct methods to compute the mass spectrum of gauge theories in the Hamiltonian formalism: (1) correlation-function scheme, (2) one-point-function scheme, and (3) dispersion-relation scheme. The first one examines spatial correlation functions as we do in the conventional Euclidean Monte Carlo simulations. The second one uses the boundary effect to efficiently compute the mass spectrum. The third one constructs the excited states and fits their energy using the dispersion relation with selecting quantum numbers. Each method has its pros and cons, and we clarify such properties in their applications to the mass spectrum for the 2-flavor massive Schwinger model at $m/g=0.1$ and $θ=0$ using the density-matrix renormalization group (DMRG). We note that the multi-flavor Schwinger model at small mass $m$ is a strongly coupled field theory even after the bosonizations, and thus it deserves to perform the first-principles numerical calculations. All these methods mostly agree and identify the stable particles, pions $π_a$ ($J^{PG}=1^{-+}$), sigma meson $σ$ ($J^{PG}=0^{++}$), and eta meson $η$ ($J^{PG}=0^{--}$). In particular, we find that the mass of $σ$ meson is lighter than twice the pion mass, and thus $σ$ is stable against the decay process, $σ\to ππ$. This is consistent with the analytic prediction using the WKB approximation, and, remarkably, our numerical results are so close to the WKB-based formula between the pion and sigma-meson masses, $M_σ/M_π=\sqrt{3}$.
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