We derive the interaction of fermions with a dynamical space–time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under diffeomorphisms. The derivation is worked out in the Hamiltonian formalism as a canonical transformation along the line of non-Abelian gauge theories. This yields a closed set of field equations for fermions, unambiguously fixing their coupling to dynamical space–time. We encounter, in addition to the well-known minimal coupling, anomalous couplings to curvature and torsion. In torsion-free geometries that anomalous interaction reduces to a Pauli-type coupling with the curvature scalar via a spontaneously emerged new coupling constant with the dimension of mass. A consistent model Hamiltonian for the free gravitational field and the impact of its functional form on the structure of the dynamical geometry space–time is discussed.

中文翻译：

---

费米子引力的协变规范规范理论

我们基于物理学的描述应该独立于参考系的假设推导出费米子与动态时空的相互作用，这意味着需要微分同胚下费米子作用的形式不变性。推导在哈密顿形式主义中作为沿非阿贝尔规范理论的规范变换得到。这产生了一组封闭的费米子场方程，明确地将它们的耦合固定到动态时空。除了众所周知的最小耦合之外，我们还会遇到曲率和扭转的异常耦合。在无扭转几何中，异常相互作用通过自发出现的具有质量维数的新耦合常数简化为与曲率标量的泡利型耦合。