反物质引力：二次量子化和拉格朗日形式
Antimatter Gravity: Second Quantization and Lagrangian Formalism
摘要：
应用CPT定理到一个落在地球上的苹果，会导致一个反苹果落在反地球上（而不是地球上）的描述。在微观层面上，弯曲时空中的狄拉克方程同时描述了自旋为1/2的粒子及其耦合到同一弯曲时空度规的反粒子（例如，描述地球的引力场的度量）。因此，在宏观层面上，电磁和引力耦合的狄拉克方程描述了苹果和反苹果同时落在地球上。因此，引力耦合狄拉克方程的粒子到反粒子的变换产生了关于“地球上的反苹果”行为的信息。然而，这个问题是加剧了这一事实，即操作的电荷共轭是更复杂的弯曲，而不是平坦的时空。我们的治疗是基于二次量子化的字段运营商，并使用拉格朗日形式主义。作为一个额外的有用的结果，我们的计算的先决条件，我们建立的狄拉克伴随在弯曲的时空的一般形式。在一个定理的基础上，我们驳斥了微小的，但潜在的重要性，粒子反粒子对称性破缺项的存在，其可能存在的文献中已调查。反物质引力实验的后果进行了讨论。
英文摘要：
The application of the CPT theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti-Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of "anti-apples on Earth". However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved as opposed to flat space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms whose possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed.
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