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Mathematics
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Mathematical Modelling in Relativity and Quantum Theory
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Mathematical Modelling in Relativity and Quantum Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 2204

Special Issue Editor

Prof. Dr. Michael M. Tung

E-Mail Website
Guest Editor
Doctor of Physics, Doctor of Mathematics, Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: theoretical physics; applied mathematics; astrophysics and cosmology; modified gravity theories

Special Issue Information

Dear Colleagues,

Nowadays, mathematical modelling is an indispensable tool for the successful description and simulation of systems in natural sciences and engineering. Within the field of theoretical physics, applications of relativity and quantum theory are at the forefront of active research and can also be combined with applied mathematics. Numerical relativity, which includes dealing with gravitational wave simulation, and quantum field theory, which describes higher order perturbative corrections of interacting particles, are utilized in  specific mathematical models of ongoing and outstanding importance. Moreover, models for global positioning systems with their engineering challenges, or simulations of elementary mechanical devices in strong gravitational fields that display unprecedented phenomena, are intriguing physical systems to model.

This Special Issue welcomes contributions on applications of relativity and quantum theory, aiming at the description and simulation of interesting physical systems in both realms.

Prof. Dr. Michael M. Tung
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • relativistic models
  • cosmology
  • analog models of gravity
  • navigational systems
  • quantum effects
  • perturbative QFT

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Published Papers (2 papers)

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Research

11 pages, 274 KiB  
Article
Defining and Analyzing New Classes Associated with (λ,γ)-Symmetrical Functions and Quantum Calculus
by Hanen Louati, Afrah Y. Al-Rezami, Abdulbasit A. Darem and Fuad Alsarari
Mathematics 2024, 12(16), 2603; https://doi.org/10.3390/math12162603 - 22 Aug 2024
Viewed by 524
Abstract
In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of (λ,γ)-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for [...] Read more.
In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of (λ,γ)-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class Sqλ,γ(x,y,z). Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes. Full article
(This article belongs to the Special Issue Mathematical Modelling in Relativity and Quantum Theory)
29 pages, 2152 KiB  
Article
A Quantum Formalism for Abstract Dynamical Systems
by Joan C. Micó
Mathematics 2024, 12(7), 1076; https://doi.org/10.3390/math12071076 - 2 Apr 2024
Viewed by 1105
Abstract
This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first-order differential equations. They are referred to as “abstract” because their dynamical variables can be of different interrelated natures, not necessarily corresponding to physics, such as [...] Read more.
This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first-order differential equations. They are referred to as “abstract” because their dynamical variables can be of different interrelated natures, not necessarily corresponding to physics, such as populations, socioeconomic variables, behavioral variables, etc. A classical linear Hamiltonian can be derived for ADS by using Dirac’s dynamics for singular Hamiltonian systems. Also, a corresponding first-order Schrödinger equation (which involves the existence of a system Planck constant particular of each system) can be derived from this Hamiltonian. However, Madelung’s reinterpretation of quantum mechanics, followed by the Bohm and Hiley work, produces no further information about the mathematical formulation of ADS. However, a classical quadratic Hamiltonian can also be derived for ADS, as well as a corresponding second-order Schrödinger equation. In this case, the Madelung reinterpretation of quantum mechanics provides a quantum Hamiltonian that does provide the quantum formulation for ADS, which provides new quantum variables interrelated dynamically with the classical variables. An application case is presented: the one-dimensional autonomous system given by the logistic dynamics. The differences between the classical and the quantum trajectories are highlighted in the context of this application case. Full article
(This article belongs to the Special Issue Mathematical Modelling in Relativity and Quantum Theory)
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