共形对称性、标准模型与引力
Conformal symmetry, SM and Gravity
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中文总结 AI 辅助
尝试将标准模型和广义相对论纳入独特量子场论，模型无相关反常，费米子谱含标准模型与镜像多重态，引入伸缩子扩大对称性，介绍代数重整化形式体系，分析共形上同调，抵消项可消除非物理粒子。
中文摘要 AI 辅助
本文是自下而上将标准模型和广义相对论纳入独特量子场论的尝试。所提出的模型尤其不存在手征规范和引力反常，当标准模型物质与引力耦合时，电流散度、能量动量张量散度和迹中不会出现此类反常。费米子谱由两个多重态组成，即标准模型（左）多重态和具有相反手性的镜像副本（右），右多重态被解释为描述暗物质世界。通过引入一个或多个伸缩子场，理论的自然对称性扩大到包含外尔不变性。介绍了代数重整化的必要形式体系，包括规范固定、鬼场、传播子和顶点及其在保证减除振幅收敛条件方面的相互作用。分析了相应的（共形）上同调，发现其为平凡的：具有伸缩子的理论中不存在非平凡的偶迹反常，但有许多平凡的，这需要在有效作用量中对应抵消项。结果表明，此类抵消项在消除理论中非物理粒子方面可发挥重要作用。
英文摘要
This paper is a bottom up attempt to incorporate the standard model and general relativity in a unique quantum field theory. The tentative model presented here in particular is free of chiral gauge and gravitational anomalies that appear in the divergence of currents, and in the divergence and trace of the energy-momentum tensor when the SM matter couples to gravity. The fermion spectrum is composed of two multiplets, the SM (left) multiplet and a mirror copy (right) with opposite handedness. The right multiplet is interpreted as describing the dark matter world. The natural symmetry of the theory is enlarged to incorporate also Weyl invariance, by introducing one or more dilaton fields. After the cosmological and theoretical motivations, the necessary formalism is introduced for algebraic renormalization: gauge fixings, ghosts, propagators and vertices and their interplay in guaranteeing the conditions for convergence of the subtracted amplitudes according to the BPHZL scheme, the Slavnov-Taylor identity and the relevant enlarged BRST symmetry. The corresponding (conformal) cohomology is analyzed and found to be trivial: there are no non-trivial even trace anomalies in theories with dilatons, but there are plenty of trivial ones, which require corresponding counterterms in the effective action. It is shown that such counterterms can play an important role in freeing the theory of unphysical particles.
