Antimatter Gravity: Second Quantization and Lagrangian Formalism

Author

Ulrich D. Jentschura, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

U. D. Jentschura, "Antimatter Gravity: Second Quantization and Lagrangian Formalism," Physics (Switzerland), vol. 2, no. 3, pp. 397 - 411, MDPI, Sep 2020.

The definitive version is available at https://doi.org/10.3390/physics2030022

Department(s)

Physics

Publication Status

Open Access

Comments

National Science Foundation, Grant PHY–1710856

Keywords and Phrases

Antimatter free-fall experiments; Antimatter gravity; CPT symmetry; Curved space-time; Dirac equation; Lorentz violation

International Standard Serial Number (ISSN)

2624-8174

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 The Authors, All rights reserved.

Creative Commons Licensing

This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Sep 2020