Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED

Chaichian, M.; Sheikh-Jabbari, M. M.; Tureanu, Anca

doi:10.1103/physrevlett.86.2716

Cited by 681 publications

(844 citation statements)

References 15 publications

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“…Кро-ме того, имеется много работ, посвященных теоретико-полевым исследованиям раз-личных аспектов квантовой механики в НКП и НКФП с обычными (коммутатив-ными) временными координатами [1]- [11]. Например, фаза Ааронова-Бома в НКП и НКФП исследовалась в работах [1]- [3], а фаза Ааронова-Кашера для частиц со спином 1/2 и спином 1 в НКП и НКФП -в работах [4], [5]. В работах [6], [7] рас-сматривались задача Ландау и эффект Хе-Мекеллара-Вилкенса как в НКП, так и в НКФП.…”

Section: Introductionunclassified

Функции Вигнера Для Задачи Ландау В Некоммутативной Квантовой Механике

Dulat¹,

Ли²,

Li³

et al. 2011

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Section: Introductionunclassified

Функции Вигнера Для Задачи Ландау В Некоммутативной Квантовой Механике

Dulat¹,

Ли²,

Li³

et al. 2011

ТМФ

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“…In [10] it was proposed the perturbative method of the construction of a gauge operator D which relates the given star product ⋆ ′ with the one ⋆ satisfying the condition (2). So, starting with the star product [5] and then gauging it with the help of [10] we end up with the desirable star product.…”

Section: Quantum Mechanics On Coordinate-dependent Noncommutative Spacesmentioning

confidence: 99%

“…The contribution of the noncommutativity in the energy spectrum (10) appears as a correction to the fine structure of the Hydrogen atom. The corresponding nonlocality is ∆x∆y ≥ θ 2 4 |m| , where m = −l, ..., l and l = 0, 1, ..., n.…”

Section: Quantum Mechanics On Coordinate-dependent Noncommutative Spacesmentioning

confidence: 99%

“…The problem is that the star product proposed in [5] does not satisfy the condition (2). To solve it we use a gauge freedom [12] in the defnition of a star product.…”

Section: Quantum Mechanics On Coordinate-dependent Noncommutative Spacesmentioning

confidence: 99%

“…In most simple case one may impose the canonical NC relations, [x ρ ,x σ ] = iθ ρσ with the constant θ ρσ being the parameters of noncommutativity. A problem with the canonical noncommutativity is that it breaks the symmetries of the physical systems, like the rotational symmetry of the Coulomb problem [2] or the Lorentz symmetry of field theoretical models [3]. The violation of symmetries is easy to understand, the left side of the postulated commutator should transform as a tensor under rotations, while the right side is a constant and does not transform.…”

Section: Introductionmentioning

confidence: 99%

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Conserved symmetries in noncommutative quantum mechanics

Kupriyanov

2014

Fortschritte der Physik

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We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in field theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. First we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time.

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From Dirac theories in curved space‐times to a variation of Dirac's large–number hypothesis

Jentschura

2014

Annalen der Physik

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Some physicists, even today, may think that it is impossible to connect relativistic quantum mechanics and general relativity [1][2][3]. This impression, however, is false, as demonstrated, among many other recent works, in an article published not long ago in this journal [4]. In order to understand the subtlety, let us remember the meaning of first [5,6], second [7,8], and third quantization (see Refs. [9][10][11]). In first quantization, what was previously a well-defined particle trajectory now becomes smeared and defines a probability density of the quantum mechanical particle. In second quantization, what was previously a well-defined functional value of a physical field at a given space-time point now becomes a field operator, which is subject to quantum fluctuations. E.g., quantum fluctuations about the flat space-time metric can be expressed in terms of the graviton field operator, for which an explicit expression can be found in Eq. (5) of Ref. [8].In third quantization, what was previously a well-defined space-time point now becomes an operator, defining a conceivably noncommutative entity, which describes space-time quantization. E.g., the emergence of the noncommutative Moyal product in quantized string theory is discussed in a particularly clear exposition in Ref. [11], in the derivation leading to Eq. (32) We thus observe that space-time quantization is not necessary, a priori, in order to combine general relativity and quantum mechanics. Indeed, before we could ever conceive to observe effects due to space-time quantization, we should first consider the leading-order coupling of the Dirac particle to a curved spacetime. Space-time curvature is visible on the classical level, and can be treated on the classical level [3]. Deviations from perfect Lorentz symmetry caused by effects other than space-time curvature may result in conceivable anisotropies of spacetime; they have been investigated by Kostelecky et al. in a series of papers (see Refs. [13][14][15] and references therein) and would be visible in tiny deviations of the dispersion relations of the relativistic particles from the predictions of Dirac theory. Measurements on neutrinos [15] can be used in order to constrain the Lorentz-violating parameters. Other recent studies concern the modification of gravitational effects under slight global violations of Lorentz symmetry [16]. Brill and Wheeler [17] were among the first to study the gravitational interactions of Dirac particles, and they put a special emphasis on neutrinos. The motivation can easily be guessed: Neutrinos, at the time, were thought to be massless and transform according to the fundamental ( ) representations of the Lorentz group. Yet, their interactions have a profound impact on cosmology [18]. Being (almost) massless, their gravitational interactions can, in principle, only be formulated on a fully relativistic footing. This situation illustrates a pertinent dilemma: namely, the gravitational potential, unlike the the Coulomb potential, cannot simply be inserted into th...

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Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED

Cited by 681 publications

References 15 publications

Функции Вигнера Для Задачи Ландау В Некоммутативной Квантовой Механике

Функции Вигнера Для Задачи Ландау В Некоммутативной Квантовой Механике

Conserved symmetries in noncommutative quantum mechanics

From Dirac theories in curved space‐times to a variation of Dirac's large–number hypothesis

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