标题： 从量子有效作用的海森几何中的重正化群流 显示英文标题

标题： Renormalization group flows from the Hessian geometry of quantum effective actions

摘要： 我们通过考虑场构型空间（所有场构型都存在于该空间中）来探索量子场论的几何视角。利用由施温格泛函的勒让德变换构造的$n$-粒子不可约有效作用量，这个构型空间可以与一个海森伯流形相关联。这使得$n$-粒子不可约有效作用量的各种性质和应用可以用几何术语重新表述。特别是，将两点源解释为调节器时，这种方法可以很容易地与函数重正化群联系起来。然后，重正化群流可以通过在这个海森伯流形上的测地线来理解。 显示英文摘要

摘要： We explore a geometric perspective on quantum field theory by considering the configuration space, where all field configurations reside. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the Schwinger functional, this configuration space can be associated with a Hessian manifold. This allows for various properties and uses of the $n$-particle irreducible effective actions to be re-cast in geometrical terms. In particular, interpreting the two-point source as a regulator, this approach can be readily connected to the functional renormalization group. Renormalization group flows are then understood in terms of geodesics on this Hessian manifold.