标题： 从构型空间上的一个 Dirac 算子得出的 Yang-Mills-Dirac 量子场论 显示英文标题

标题： A Yang-Mills-Dirac Quantum Field Theory Emerging From a Dirac Operator on a Configuration Space

摘要： 从一个定义在 $SU(2)$ 规范联络构型空间上的Dirac算子出发，我们考虑它在内自同构下的扰动。 我们证明了一类特定的扭变内扰动会得到一个Dirac算子，其平方给出了Yang-Mills量子场论的哈密顿量，并耦合到由一形式费米子组成的费米子部分。 然后我们证明了，如果在基本的三维流形上存在度规，那么存在构型空间的一种基变换，使得变换后的费米子部分由不再是单形式的费米子组成。 显示英文摘要

摘要： Starting with a Dirac operator on a configuration space of $SU(2)$ gauge connections we consider its fluctuations with inner automorphisms. We show that a certain type of twisted inner fluctuations leads to a Dirac operator whose square gives the Hamiltonian of Yang-Mills quantum field theory coupled to a fermionic sector that consist of one-form fermions. We then show that if a metric exists on the underlying three-dimensional manifold then there exists a change of basis of the configuration space for which the transformed fermionic sector consists of fermions that are no-longer one-forms.