论文标题
重力接触相互作用和有效田间理论中Weyl转化的物理等效性
Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory
论文作者
论文摘要
标量和重力的理论，具有非最小相互作用，$ \ sim（m_p^2 +f（ϕ））r +l（ϕ）$具有重力交换引起的接触项。这些术语在带有顶点$ \ propto q^2 $的单个粒子简化图中产生，该术语取消了Feynman繁殖者分母$ 1/q^2 $，并且在其他各种物理环境中都很熟悉。在重力中，这些导致动作中的其他术语，例如$ \ sim f（ϕ）t_μ^μ（ϕ）/m_p^2 $和$ f（ϕ）\ partial^2 f（ϕ）/m_p^2 $。接触项等同于通过去除非最小相互作用的Weyl转化获得的诱导算子，留下了最小的爱因斯坦 - 希尔伯特重力作用。这明确证明了在经典和量子上，在Weyl转换下，动作的不同表示的等效性。为了避免这种“隐藏的接触术语”，被迫进入最小的爱因斯坦 - 希尔伯特代表。
Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +F(ϕ) )R +L(ϕ)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim F(ϕ) T_μ^μ(ϕ)/M_P^2$ and $F(ϕ)\partial^2 F(ϕ)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.
