论文标题
紫外线完全量子场理论与分数操作员
Ultraviolet-complete quantum field theories with fractional operators
论文作者
论文摘要
我们探索量子场理论，该理论具有分数d'Alembertian $ \ box^γ$。具有衍生依赖性电位的标量场理论和量规理论对于分数功率$ 1 <γ\ leq 2 $，可用于$γ> 2 $的单循环超级质量的超级符号，如果有人引入杀手企业。单位性是通过将动力学术语拆分成大量分数操作员的乘积来实现的，如果需要，最终将质量发送到零。还讨论了分数量子重力，并发现以$ 2 <γ\ leq 4 $和可以$γ> 4 $的价格为$ 2 <γ\ leq 4 $，可超级肾上腺质量。为了使其统一，我们将分裂程序与假子的Anselmi-Piva程序的分数概括相结合。在更广泛的应用程序的新技术结果中，我们重点介绍了D'Alembertian任意权力的Leibniz规则和Källén-Lehmann代表，用于具有任意分支削减数量的传播器。
We explore quantum field theories with fractional d'Alembertian $\Box^γ$. Both a scalar field theory with a derivative-dependent potential and gauge theory are super-renormalizable for a fractional power $1<γ\leq 2$, one-loop super-renormalizable for $γ>2$ and finite if one introduces killer operators. Unitarity is achieved by splitting the kinetic term into the product of massive fractional operators, eventually sending the masses to zero if so desired. Fractional quantum gravity is also discussed and found to be super-renormalizable for $2<γ\leq 4$ and one-loop super-renormalizable for $γ>4$. To make it unitary, we combine the splitting procedure with a fractional generalization of the Anselmi-Piva procedure for fakeons. Among new technical results with wider applications, we highlight the Leibniz rule for arbitrary powers of the d'Alembertian and the Källén-Lehmann representation for a propagator with an arbitrary number of branch cuts.
