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Axioms
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Mathematical Aspects of Quantum Field Theory and Quantization
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Mathematical Aspects of Quantum Field Theory and Quantization

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Hilbert’s Sixth Problem".

Deadline for manuscript submissions: 30 January 2026 | Viewed by 4059

Special Issue Editor

Dr. Alexandre Landry

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, Canada
Interests: teleparallel gravity and geometry; quantization; special functions; fundamental quantized particles; physical quantum process; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aims of this Special Issue on the mathematical aspects of QFT and quantum mechanics are to present and highlight the most recent research developments in this topic. This Special Issue will specifically target mathematical methods and, more specifically, new solutions to differential equations and special functions of the Schrödinger, Klein–Gordon, Dirac and Proca equations. This differential equation list is not exhaustive. We also want to emphasize perturbations in QFT, the WKB method, more general second-order approximations and, more generally, quantum theories.

Indeed, there have recently been mathematical innovations in these areas, notably new classes of special functions that can be used very well for various approaches to quantum perturbations. We hope that the new contributions will also be able to interconnect with these same recent advances. In addition, we are also open to contributions regarding mathematical innovations in quantum gravity. This subject is interesting and in full development; this would complete this Special Issue well.

We look forward to receiving your contributions, and they will be considered seriously.

Best regards,

Dr. Alexandre Landry
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • quantization
  • Schrodinger
  • Klein–Gordon
  • Dirac
  • quantum field theory
  • special functions
  • perturbations
  • WKB approximations
  • quantum gravity

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Published Papers (3 papers)

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Research

11 pages, 286 KiB  
Article
Vector Meson Spectrum from Top-Down Holographic QCD
by Mohammed Mia, Keshav Dasgupta, Charles Gale, Michael Richard and Olivier Trottier
Axioms 2025, 14(1), 66; https://doi.org/10.3390/axioms14010066 - 16 Jan 2025
Viewed by 549
Abstract
We elaborate on the brane configuration that gives rise to a QCD-like gauge theory that confines at low energies and becomes scale invariant at the highest energies. In the limit where the rank of the gauge group is large, a gravitational description emerges. [...] Read more.
We elaborate on the brane configuration that gives rise to a QCD-like gauge theory that confines at low energies and becomes scale invariant at the highest energies. In the limit where the rank of the gauge group is large, a gravitational description emerges. For the confined phase, we obtain a vector meson spectrum and demonstrate how a certain choice of parameters can lead to quantitative agreement with empirical data. Full article
(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)
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20 pages, 269 KiB  
Article
Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment
by Alina Ivashkevich, Viktor Red’kov and Artur Ishkhanyan
Axioms 2025, 14(1), 35; https://doi.org/10.3390/axioms14010035 - 3 Jan 2025
Viewed by 1272
Abstract
We start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wave function consists of a two-rank symmetric tensor [...] Read more.
We start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wave function consists of a two-rank symmetric tensor and a three-rank tensor that is symmetric in two indices. We apply the general method for performing the nonrelativistic approximation, which is based on the structure of the 50×50 matrix Γ0 of the main equation. Using the 7th-order minimal equation for the matrix Γ0, we introduce three projective operators. These operators permit us to decompose the complete wave function into the sum of three parts: one large part and two smaller parts in the nonrelativistic approximation. We have found five independent large variables and 45 small ones. To simplify the task, by eliminating the variables related to the 3-rank tensor, we have derived a relativistic system of second-order equations for the 10 components related to the symmetric tensor. We then take into account the decomposition of these 10 variables into linear combinations of large and small ones. In accordance with the general method, we separate the rest energy in the wave function and specify the orders of smallness for different terms in the arising equations. Further, after performing the necessary calculations, we derive a system of five linked equations for the five large variables. This system is presented in matrix form, which has a nonrelativistic structure, where the term representing additional interaction with the external magnetic field through three spin projections is included. The multiplier before this interaction contains the basic magnetic moment and an additional term due to the anomalous magnetic moment. The latter characteristic is treated as a free parameter within the hypothesis. Full article
(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)
21 pages, 401 KiB  
Article
From Uncertainty Relations to Quantum Acceleration Limits
by Carlo Cafaro, Christian Corda, Newshaw Bahreyni and Abeer Alanazi
Axioms 2024, 13(12), 817; https://doi.org/10.3390/axioms13120817 - 22 Nov 2024
Cited by 1 | Viewed by 800
Abstract
The concept of quantum acceleration limit has been recently introduced for any unitary time evolution of quantum systems under arbitrary nonstationary Hamiltonians. While Alsing and Cafaro used the Robertson uncertainty relation in their derivation, employed the Robertson–Schrödinger uncertainty relation to find the upper [...] Read more.
The concept of quantum acceleration limit has been recently introduced for any unitary time evolution of quantum systems under arbitrary nonstationary Hamiltonians. While Alsing and Cafaro used the Robertson uncertainty relation in their derivation, employed the Robertson–Schrödinger uncertainty relation to find the upper bound on the temporal rate of change of the speed of quantum evolutions. In this paper, we provide a comparative analysis of these two alternative derivations for quantum systems specified by an arbitrary finite-dimensional projective Hilbert space. Furthermore, focusing on a geometric description of the quantum evolution of two-level quantum systems on a Bloch sphere under general time-dependent Hamiltonians, we find the most general conditions needed to attain the maximal upper bounds on the acceleration of the quantum evolution. In particular, these conditions are expressed explicitly in terms of two three-dimensional real vectors, the Bloch vector that corresponds to the evolving quantum state and the magnetic field vector that specifies the Hermitian Hamiltonian of the system. For pedagogical reasons, we illustrate our general findings for two-level quantum systems in explicit physical examples characterized by specific time-varying magnetic field configurations. Finally, we briefly comment on the extension of our considerations to higher-dimensional physical systems in both pure and mixed quantum states. Full article
(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)
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