We build the fully relativistic quantum field theory related to the asymmetric Dirac fields first presented in a prequel to this work. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and ‘negative’ frequency plane wave solutions’ dispersion relations are no longer degenerate. At the second quantization level, we show that this implies that particles and antiparticles sharing the same wave number have different energies and momenta. In spite of that, we prove that by properly fixing the values of the relativistic invariants that define the asymmetric Dirac free field Lagrangian density, we can build a consistent, fully relativistic, and renormalizable quantum electrodynamics (QED) that is empirically equivalent to the standard QED. We discuss the reasons and implications of this non-trivial equivalence, exploring qualitatively other scenarios in which the asymmetric Dirac fields may lead to beyond the standard model predictions. We give a complete account of how the asymmetric Dirac fields and the corresponding annihilation and creation operators transform under improper Lorentz transformations (parity and time reversal operations) and under the charge conjugation operation. We also prove that the present theory respects the CPT theorem.

中文翻译：

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不对称粒子-反粒子狄拉克方程：第二次量子化


我们建立了与不对称狄拉克场相关的完全相对论量子场论，该场论首次在这项工作的前传中提出。这些场是非对称狄拉克方程的解，这是一个类洛伦兹协变狄拉克方程，其正和“负”频率平面波解的色散关系不再简并。在第二量子化水平上，我们表明这意味着共享相同波数的粒子和反粒子具有不同的能量和动量。尽管如此，我们证明，通过正确固定定义不对称狄拉克自由场拉格朗日密度的相对论不变量的值，我们可以建立一致的、完全相对论的、可重整化的量子电动力学（QED），该量子电动力学在经验上与标准等效量子ED。我们讨论了这种非平凡等价性的原因和含义，定性地探索了非对称狄拉克场可能导致超出标准模型预测的其他场景。我们完整地描述了非对称狄拉克场以及相应的湮没和创造算子在不正确的洛伦兹变换（宇称和时间反转运算）和电荷共轭运算下如何变换。我们还证明了当前的理论尊重 CPT 定理。