The Dirac Electron: From Quantum Chemistry to Holistic Cosmology

Maruani, J.

doi:10.1002/jccs.201500374

Cited by 16 publications

(4 citation statements)

References 44 publications

(6 reference statements)

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“…where the curved-space Dirac matrices γ µ fulfill "local" commutation relations given in Eq. (15). These depend on the space-time coordinates.…”

Section: Covariant Gravitational Couplingmentioning

confidence: 99%

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Equivalence principle for antiparticles and its limitations

Jentschura

2019

Int. J. Mod. Phys. A

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We investigate the particle-antiparticle symmetry of the gravitationally coupled Dirac equation, both on the basis of the gravitational central-field problem and in general curved space-time backgrounds. First, we investigate the central-field problem with the help of a Foldy-Wouthuysen transformation. This disentangles the particle from the antiparticle solutions, and leads to a "matching relation" of the inertial and the gravitational mass, which is valid for both particles as well as antiparticles. Second, we supplement this derivation by a general investigation of the behavior of the gravitationally coupled Dirac equation under the discrete symmetry of charge conjugation, which is tantamount to a particle→antiparticle transformation. Limitations of the Einstein equivalence principle due to quantum fluctuations are discussed. In quantum mechanics, the question of where and when in the Universe an experiment is being performed, can only be answered up to the limitations implied by Heisenberg's Uncertainty Principle, questioning an assumption made in the original formulation of the Einstein equivalence principle. Furthermore, at some level of accuracy, it becomes impossible to separate non-gravitational from gravitational experiments, leading to further limitations.

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“…where the curved-space Dirac matrices γ µ fulfill "local" commutation relations given in Eq. (15). These depend on the space-time coordinates.…”

Section: Covariant Gravitational Couplingmentioning

confidence: 99%

“…14 For an illustrative and interpretive discussion of some interesting properties of the Dirac equation, see Ref. 15.…”

Section: Introductionmentioning

confidence: 99%

Equivalence principle for antiparticles and its limitations

Jentschura

2019

Int. J. Mod. Phys. A

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“…If one did not invoke the positive-energy projection operators in MCDF codes, then, for a system as simple as helium, nonsensical results would be obtained. Namely, one of the electrons could undergo a quantum jump into the positive-energy continuum, the other, into the negative-energy continuum, with the sum of the energies of the two continuum states (final state of the two-electron nonradiative transition) being equal to the sum of the two bound-state energies of the helium atom from which the transition started [3,8,9]. The "Brown-Ravnhall disease" is of course addressed, on the theoretical level, by invoking the Dirac sea, or, alternatively, by invoking the reinterpretation principle and quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

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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“…Devido à notação introduzida por Paul Dirac, tais vetores são usualmente chamados kets. 42 Em suma, tanto as "funções de onda" quanto os "vetores de estado" (ou kets) representam os estados de um dado sistema físico de forma completa e equivalente, uma vez que as leis da MQ descrevem como os vetores de estado e as funções de onda evoluem no tempo. Estes objetos matemáticos abstratos, kets e funções de onda, permitem o cálculo da probabilidade de se obter resultados específicos em um experimento concreto.…”

Section: Superposição De Estados Quânticos E Coerênciaunclassified

Quantum Information and Nuclear Magnetic Resonance Parameters

Lino¹,

Ramalho²

2018

Rev. Virtual Quim

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Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing. Quantum information processing promises to extend today's computing resources. Quantum computers, theoretically, could solve problems much more quickly than any classic computer. Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms. In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols. The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area. Therefore, nuclear spins are picked out as good candidates for quantum bits. In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.

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The Dirac Electron: From Quantum Chemistry to Holistic Cosmology

Cited by 16 publications

References 44 publications

Equivalence principle for antiparticles and its limitations

Equivalence principle for antiparticles and its limitations

Antimatter Gravity: Second Quantization and Lagrangian Formalism

Quantum Information and Nuclear Magnetic Resonance Parameters

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