Nonlocal Phenomena in Quantum Mechanics with Fractional Calculus

Atman, Kazım Gökhan; Şirin, Hüseyin

doi:10.1016/s0034-4877(20)30075-6

Cited by 16 publications

(5 citation statements)

References 14 publications

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“…Here, α a p and a p a † represent the fractional creation/annihilation operators which are interpreted as the increasing or decreasing the energy of state by a fractional unit of energy [43].…”

Section: Fractional Massive Scalar Fieldsmentioning

confidence: 99%

Quantization of nonlocal fields via fractional calculus

Atman

Şirin

2022

Phys. Scr.

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In this study, we investigate the effect of nonlocality in quantum mechanics and propose a fractional approach the theory of quantized fields. For this purpose, we embedded the fractional calculus to broaden theory of quantum fields since the integral and derivative operators are nonlocal in fractional calculus.Additionally, quantum entanglement is discussed to gain comprehension of nonlocality in the foundation of quantum mechanics. Besides, fractional Lagrangian formalism was presented due to fact that the Lagrangian density is the starting point to establish a field theory.Furthermore, to make fractional field operators quantum mechanical, equal-time commutator have been defined for the these operators in terms of Caputo fractional derivative. Thus, a scheme of quantization of fractional fields is introduced and general aspects of the method is illustrated with the theory of massive scalar fields. This approach laid out to a successful generalization of the quantum field theory which is coherent with the standard formalism. Consequently, we developed promising concept for a quantum field theory by introducing nonlocality into standard mathematical formalism.

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Section: Fractional Massive Scalar Fieldsmentioning

confidence: 99%

Quantization of nonlocal fields via fractional calculus

Atman

Şirin

2022

Phys. Scr.

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“…A generalization of this theory has led to the rise of the field of fractional differential equations (FDEs) [1], extending the conventional framework of differential equations by incorporating fractional derivatives. This extension has countless applications in various scientific fields, such as quantum mechanics [3,4,5,6,7,8], electrodynamics [9,10,11,12], economics [13,14,15,16], engineering [17,18,19], biology [20,21], and geology [22].…”

Section: Introductionmentioning

confidence: 99%

Caputo fractional standard map: Scaling invariance analyses

Borin

2024

Chaos, Solitons & Fractals

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“…Fractional calculus has been applied in many areas and has proven its capacity to describe several physical phenomena associated with the memory effect. It models many real-life phenomena involving non-local behavior in biology, physics, etc [1][2][3][4]. Many researchers have shown the great importance of non-local operators in mathematical epidemiology [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A new numerical method to solve fractional differential equations in terms of Caputo-Fabrizio derivatives

Mahatekar¹,

Scindia²,

Kumar

2023

Phys. Scr.

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In this article, we derive a new numerical method to solve fractional differential equations containing Caputo-Fabrizio derivatives. The fundamental concepts of fractional calculus, numerical analysis, and fixed point theory form the basis of this study. Along with the derivation of the algorithm of the proposed method, error and stability analyses are performed briefly. To explore the validity and effectiveness of the proposed method, several examples are simulated, and the new solutions are compared with the outputs of the previously published two-step Adams-Bashforth method.

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Nonlocal Phenomena in Quantum Mechanics with Fractional Calculus

Cited by 16 publications

References 14 publications

Quantization of nonlocal fields via fractional calculus

Quantization of nonlocal fields via fractional calculus

Caputo fractional standard map: Scaling invariance analyses

A new numerical method to solve fractional differential equations in terms of Caputo-Fabrizio derivatives

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