Scientists have developed a local field redefinition that simplifies the quantum field theory of fermions in curved and non-inertial backgrounds. This new formulation allows canonical structures — such as the Lagrangian, the inner product, and equal-time anticommutation relations — to be expressed in their standard Minkowski form, as used in inertial Cartesian coordinates in Minkowski spacetime. This advance is crucial because quantum field theory in curved spacetimes often involves background- and foliation-dependent quantities, complicating their analysis and quantification.

The work begins with the generally covariant Dirac action, minimally coupled to a spin-1 gauge field. From this, the Lagrangian, the fermionic inner product, and the quantization rule are derived using an Arnowitt-Deser-Misner (ADM) decomposition in arbitrary coordinates. The key to the method lies in identifying the generalized temporal gamma matrix as the common geometric factor governing the canonical temporal structure of all these quantities. By transforming this gamma matrix to its standard Minkowski form through the field redefinition, the fermionic inner product and the equal-time anticommutation relations adopt their standard expressions, transferring the explicit background and foliation dependence to the transformed fermionic field operators and Lagrangian.

This field redefinition necessarily involves a local rescaling and the fixing of a local Lorentz frame. The procedure restores the conventional canonical normalization from standard Minkowski spacetime, used for fermionic mode quantization and occupation-number operators. As a result, the transformed Lagrangian takes on a generalized first-order Schrödinger form, which includes the familiar rest-energy term and spacetime-magnetic couplings, as well as the leading non-relativistic limit, where temporal derivatives are separated from spatial ones. This facilitates physical interpretation and calculations in complex gravitational scenarios.