从谱DSE得到的$ϕ^4$ -理论中的谱函数
Spectral functions in the $ϕ^4$-theory from the spectral DSE
摘要：
我们开发了一个非微扰的功能框架，用于计算强关联系统中的实时关联函数。该框架是基于关联函数和维正则化的频谱表示。因此，这里的非微扰谱重整化设置尊重手头的理论的所有对称性。特别地，这包括时空对称性以及内部对称性，例如手征对称性和规范对称性。光谱重正化可以应用于一般的功能方法，如功能重正化组，戴森-Schwinger方程，和两个或$n$ -粒子不可约的方法。作为应用，我们从谱Dyson-Schwinger方程计算了$2+1$维的$ϕ^4$ -理论中标量场的全谱、非微扰函数。我们还计算了全$ϕ^4$ -顶点的$s$ -通道谱函数.
英文摘要：
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation setup here respects all symmetries of the theories at hand. In particular this includes space-time symmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalisation can be applied within general functional approaches such as the functional renormalisation group, Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As an application we compute the full, non-perturbative, spectral function of the scalar field in the $ϕ^4$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full $ϕ^4$-vertex in this theory.
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