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Antimatter Gravity: Second Quantization and Lagrangian Formalism

1
Department of Physics, Missouri University of Science and Technology, Rolla, MO 65409, USA
2
MTA–DE Particle Physics Research Group, P.O. Box 51, H–4001 Debrecen, Hungary
3
MTA Atomki, P.O. Box 51, H–4001 Debrecen, Hungary
Received: 17 July 2020 / Revised: 28 August 2020 / Accepted: 31 August 2020 / Published: 3 September 2020
(This article belongs to the Special Issue Beyond the Standard Models of Physics and Cosmology)
The application of the CPT (charge-conjugation, parity, and time reversal) 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 in which possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed. View Full-Text
Keywords: antimatter gravity; CPT symmetry; antimatter free-fall experiments; Lorentz violation; Dirac equation; curved space-time antimatter gravity; CPT symmetry; antimatter free-fall experiments; Lorentz violation; Dirac equation; curved space-time
MDPI and ACS Style

Jentschura, U.D. Antimatter Gravity: Second Quantization and Lagrangian Formalism. Physics 2020, 2, 397-411. https://0-doi-org.brum.beds.ac.uk/10.3390/physics2030022

AMA Style

Jentschura UD. Antimatter Gravity: Second Quantization and Lagrangian Formalism. Physics. 2020; 2(3):397-411. https://0-doi-org.brum.beds.ac.uk/10.3390/physics2030022

Chicago/Turabian Style

Jentschura, Ulrich D. 2020. "Antimatter Gravity: Second Quantization and Lagrangian Formalism" Physics 2, no. 3: 397-411. https://0-doi-org.brum.beds.ac.uk/10.3390/physics2030022

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