Gravitationally coupled Dirac equation for antimatter

Jentschura, U. D.

doi:10.1103/physreva.87.032101

Cited by 12 publications

(10 citation statements)

References 24 publications

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“…It is easy to show that Equation 13generalizes to all orders in the AB (x) parameters, which justifies our ansatz given in Equation (11). The result is that the flat-space γ 0 matrix can be used in curved space, just like in flat space, in order to construct the Dirac adjoint.…”

Section: Dirac Adjoint For Curved Space-timessupporting

confidence: 62%

“…Corresponding investigations have been initiated in a series of recent publications [10][11][12][13]. One may ask whether the dynamics of particles and antiparticles differ in a central, static, gravitational field, but also, if there are any small higher-order effects breaking the particle-antiparticle symmetry under the gravitational interaction.…”

Section: Introductionmentioning

confidence: 99%

“…One may ask whether the dynamics of particles and antiparticles differ in a central, static, gravitational field, but also, if there are any small higher-order effects breaking the particle-antiparticle symmetry under the gravitational interaction. For the central gravitational field, this question has been answered in [10][11][12], with the result being that the Dirac particle and antiparticle behave exactly the same in a central gravitational field, due to a perfect particle-antiparticle symmetry which extends to the relativistic and curved-space-time corrections to the equations of motion. For a de Sitter space-time, which has constant curvature, we refer to [14].…”

Section: Introductionmentioning

confidence: 99%

“…Related calculations have recently been considered in other contexts [25,28,29]. The question of whether such parity-and particle-antiparticle symmetry violating terms could exist in higher orders in the momentum expansion has been answered negatively in [11], but only for a static central gravitational field, and in [30], still negatively, for combined static, central gravitational, and electrostatic fields.…”

Section: Introductionmentioning

confidence: 99%

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Antimatter Gravity: Second Quantization and Lagrangian Formalism

Jentschura

2020

Physics

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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.

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Section: Dirac Adjoint For Curved Space-timessupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Antimatter Gravity: Second Quantization and Lagrangian Formalism

Jentschura

2020

Physics

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“…(For a truly curved space, the notation g µν has been proposed in Refs. [45,46] in order to distinguish the curvedspace quantities from the flat-space ones.) Theγ µ are thus intermediate in between the usual flat-space Dirac matrices, and the curved-space matrices, for which the notation g µν has been proposed in Refs.…”

Section: Discussionmentioning

confidence: 99%

Neutrino splitting for Lorentz-violating neutrinos: Detailed analysis

Somogyi

Nándori

2019

Phys. Rev. D

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Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E ≈ | p| v, where E is the energy, p is the momentum and v = √ 1 + δ > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (ν → ν + e − + e + ) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter δ can be derived. Here, we investigate a related process, νi → νi + ν f + ν f , where νi is an incoming neutrino mass eigenstate, while ν f is the final neutrino mass eigenstate, with a superluminal velocity that is slightly slower than that of the initial state. This process is kinematically allowed if the Lorentz-violating parameters at high energy differ for the different neutrino mass eigenstates. Neutrino splitting is not subject to any significant energy threshold condition and could yield quite a substantial contribution to decay and energy loss processes at high energy, even if the differential Lorentz violation among neutrino flavors is severely constrained by other experiments. We also discuss the SU (2)L-gauge invariance of the superluminal models and briefly discuss the use of a generalized vierbein formalism in the formulation of the Lorentz-violating Dirac equation.

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Foldy–Wouthuysen transformation, scalar potentials and gravity

Noble

2014

J. Phys. A: Math. Theor.

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We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac-Coulomb and the Dirac-Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and "chiral" approaches to the Foldy-Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations ("chiral" Foldy-Wouthuysen transformations). Despite their interesting algebraic properties, we find that "chiral" Foldy-Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy-Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the 1/r-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame ("Mashhoon term").

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Gravitationally coupled Dirac equation for antimatter

Cited by 12 publications

References 24 publications

Antimatter Gravity: Second Quantization and Lagrangian Formalism

Antimatter Gravity: Second Quantization and Lagrangian Formalism

Neutrino splitting for Lorentz-violating neutrinos: Detailed analysis

Foldy–Wouthuysen transformation, scalar potentials and gravity

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