弯曲与非惯性背景上的费米子量子场论：标准闵可夫斯基形式
Fermion quantum field theory on curved and non-inertial backgrounds in standard-Minkowski form
- Universität Ulm（乌尔姆大学）
- Yokohama National University（横滨国立大学）
- German Aerospace Center (DLR)（德国航空航天中心）
- ClockWerQ GmbH（ClockWerQ有限公司）
- Wayne State University（韦恩州立大学）
- Technische Universität Darmstadt（达姆施塔特工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过局域场重定义将弯曲与非惯性背景上的费米子量子场论正则结构转化为标准闵可夫斯基形式，恢复传统正则归一化，并导出广义一阶薛定谔形式及非相对论极限。
AI中文摘要：
弯曲与非惯性背景上的量子场论中，正则拉格朗日量、超曲面内积与双线性形式，以及等时反对易关系均包含依赖于背景和叶状结构的量。在本工作中，我们确定了一个局域费米子场重定义，将这些正则结构转化为其标准闵可夫斯基形式，即它们在闵可夫斯基时空笛卡尔惯性坐标中所采取的形式，其中第零世界坐标被认定为时间坐标。从一般协变的狄拉克作用量出发，该作用量最小耦合到自旋为1的规范场，我们在阿诺维特-德塞尔-米斯纳分解中推导了相应的拉格朗日量、费米子内积和量子化规则，并以任意世界坐标表述。我们将广义时间伽马矩阵识别为控制这三个量之正则时间结构的共同几何因子。通过场重定义，我们将此广义时间伽马矩阵变换为其标准闵可夫斯基形式，从而将费米子内积和等时反对易关系映射到其标准闵可夫斯基表达式，同时将显式的背景和叶状结构依赖性转移到变换后的拉格朗日量和费米子场算符中。我们证明，这样的场重定义必然包含局域重标度和局域洛伦兹框架的固定。此过程恢复了用于费米子模式量子化和占据数算符的标准闵可夫斯基时空中的传统正则归一化。变换后的拉格朗日量因此呈现广义一阶薛定谔形式，导致熟悉的静止能量项和时空磁耦合，以及领先的非相对论极限，其中时间导数与空间导数被分离。
英文摘要：
Quantum field theory on curved and non-inertial backgrounds contains background- and foliation-dependent quantities in the canonical Lagrangian, the hypersurface inner product and bilinear form, as well as in the equal-time anti-commutation relations. In this work, we determine a local fermion-field redefinition that brings these canonical structures into their standard-Minkowski forms, i. e., the forms they assume in Cartesian inertial coordinates on Minkowski spacetime, where the zeroth world coordinate is identified as the coordinate of time. Starting from the generally covariant Dirac action minimally coupled to a spin-1 gauge field, we derive the corresponding Lagrangian, fermionic inner product, and quantization rule in an Arnowitt-Deser-Misner decomposition, formulated in arbitrary world coordinates. We identify the generalized temporal gamma matrix as the common geometric factor governing the canonical temporal structure of all three quantities. Using a field redefinition, we transform this generalized temporal gamma matrix to its standard-Minkowski form, thereby mapping the fermionic inner product and the equal-time anti-commutation relation to their standard-Minkowski expressions, while transferring the explicit background and foliation dependence to the transformed Lagrangian and fermion-field operators. We show that such a field redefinition necessarily consists of a local rescaling and a fixing of the local Lorentz frame. This procedure restores the conventional canonical normalization from standard-Minkowski spacetime used for fermionic mode quantization and occupation-number operators. The transformed Lagrangian consequently assumes a generalized first-order Schrödinger form, leading to the familiar rest-energy term and spacetime-magnetic couplings, as well as to the leading non-relativistic limit, in which temporal derivatives are separated from spatial ones.
