Dirac equation in the curved spacetime and generalized uncertainty principle: A fundamental quantum mechanical approach with energy-dependent potentials

Yeşiltaş, Özlem

doi:10.1140/epjp/i2019-12694-x

Cited by 13 publications

(7 citation statements)

References 44 publications

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“…Although previous work has proposed the generalized uncertainty principle (GUP) as a form of making the Heisenberg inequalities be compatible with a minimum length (e.g., refs. [1,14,28,59]), in the PC approach the GUP is not needed as the PC size l PC is defined by the finite value of I SM P and not as a result of the Heisenberg inequalities. In the PC approach, the quantum uncertainty is expressed by the Heisenberg inequalities of Eq.…”

Section: Discussionmentioning

confidence: 99%

Darwinian standard model of physics obtains general relativity

Lori

2022

Quantum Inf Process

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A Darwinian perspective of the standard model of physics (SMP) quantum fields (QFs) is proposed, called the physics-cell (PC) approach. Because Darwinian evolution is not deterministic, the PC approach allows for the violation of the charge-parity-time symmetry. In the PC approach, the SMP laws are contained in the PCs which receive and emit QFs through the PCs’ outer surface which is necessarily constrained by Bekenstein’s surface-information limit. The establishment of gauge invariance-compatible communication protocol-agreements between the PCs obtains an average correlation of QFs that is equivalent to an asymmetric metric tensor with the symmetric component being equivalent to general relativity and the anti-symmetric component being very small but still large enough to allow for enough ex-nihilo mass-creation to explain dark matter. Based on experimental data, the PC minimum-size is $$1.5\cdot 10^{-31}$$ 1.5 · 10 - 31 m which is similar to the scale at which the grand unified theory force convergence occurs. Plus, the cosmological constant energy density is equal to the energy density of the discreteness-correction QF alterations that constitute the dark energy and are caused by the finiteness of the PC time-step which equals $$5.0\cdot 10^{-40}$$ 5.0 · 10 - 40 s, hence obtaining a PC maximum information processing rate of $$6.6\cdot 10^{47}$$ 6.6 · 10 47 qubit/s. Moreover, the PC approach obtains that the minimum mass for black holes is $$2.1 \cdot 10^{9}$$ 2.1 · 10 9 larger than the maximum mass for which the no-hiding theorem can apply and that the maximum capacity for quantum computers is about $$29.0 \cdot 10^{12}$$ 29.0 · 10 12 qubit.

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Section: Discussionmentioning

confidence: 99%

Darwinian standard model of physics obtains general relativity

Lori

2022

Quantum Inf Process

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“…In [2], the author studied the Dirac equation in the context of generalized uncertainty principle, and, in [3], it has been introduced a new generalized momentum operator taking into account, among others, the extended uncertainty principle.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

2022

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In the present study, we investigate the existence of the solutions to a type of uncertain differential equations subject to nonlocal derivatives. The approach is based on the application of an extended Krasnosel’skii fixed point theorem valid on fuzzy metric spaces. With this theorem, we deduce that the problem of interest has a fuzzy solution, which is defined on a certain interval. Our approach includes the consideration of a related integral problem, to which the above-mentioned tools are applicable. We finish with some physical motivations.

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“…According to our knowledge, only a limited number of studies have considered the effect of the extended uncertainty relation on quantum mechanical problems [21][22][23][24][25][26][27][28][29][30][31][32]. More recently, the rate of Schwinger pair production due to an external electric field in the presence of EUP was studied in [33,34].…”

Section: Introductionmentioning

confidence: 99%

Bound-state solutions of the two-dimensional Dirac equation with Aharonov–Bohm-Coulomb interaction in the presence of extended uncertainty principle

2020

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The Dirac equation in the presence of Aharonov–Bohm-Coulomb interaction is studied in the framework of the extended uncertainty principle. The equation governing the dynamics of the system is reduced to a differential equation which is solved in terms of the hypergeometric functions as the wave functions of the system. Expressions for the bound-state energies are also obtained analytically. A brief graphical evaluation of our results is also presented.

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Dirac equation in the curved spacetime and generalized uncertainty principle: A fundamental quantum mechanical approach with energy-dependent potentials

Cited by 13 publications

References 44 publications

Darwinian standard model of physics obtains general relativity

Darwinian standard model of physics obtains general relativity

Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

Bound-state solutions of the two-dimensional Dirac equation with Aharonov–Bohm-Coulomb interaction in the presence of extended uncertainty principle

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