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Mathematical Aspects of Quantum Field Theory and Quantization, 2nd Edition
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Mathematical Aspects of Quantum Field Theory and Quantization, 2nd Edition

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1430

Editor

Dr. Alexandre Landry

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, Canada
Interests: general relativity; teleparallel gravity and alternatives theories; gravitational solutions; cosmology; alternative solutions in gravitational physics; mathematical physics; quantum gravity theories
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue on the mathematical aspects of QFT and quantum mechanics aims to present and highlight the most recent research developments related to this topic, specifically targeting mathematical methods and, more specifically, new solutions to differential equations and special functions of the Schrödinger, Klein–Gordon, Dirac and Proca equations, though this 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 to this Issue will also interconnect with these same recent advances. In addition, we are also open to contributions regarding mathematical innovations in quantum gravity, an interesting and fully developed subject, which would complete this Special Issue well.

We look forward to receiving your contributions, which will be considered for publication 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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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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Related Special Issue

Published Papers (2 papers)

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Research

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14 pages, 503 KB  
Article
The Double-Slit Experiment in the Bivector Standard Model
by Bryan Sanctuary
Axioms 2026, 15(6), 417; https://doi.org/10.3390/axioms15060417 - 4 Jun 2026
Cited by 1 | Viewed by 556
Abstract
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern [...] Read more.
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern is reproduced while the phase is attributed to an internal bivector clock carried by the electron. In this approach, each electron remains localized and produces a single detection event, while the familiar fringe pattern emerges statistically from the accumulation of many impacts. Interference arises from the comparison of clock phases associated with geometrically distinct paths, rather than from the superposition of spatial waves. The resulting probability distribution recovers the standard two-slit interference factor, the single-slit diffraction envelope, and the usual fringe-spacing relation in the Fraunhofer regime. The de Broglie wavelength emerges as the spatial manifestation of this transported phase. This formulation provides a geometric account of the origin of phase in single-electron interference, consistent with standard results while offering a distinct physical interpretation. Full article
(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization, 2nd Edition)
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Review

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16 pages, 312 KB  
Review
Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity
by Alexandre Landry
Axioms 2026, 15(6), 427; https://doi.org/10.3390/axioms15060427 - 8 Jun 2026
Viewed by 596
Abstract
We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string [...] Read more.
We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string theory, and asymptotic safety, highlighting their conceptual challenges. Motivated by these issues, we outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than curvature. This framework naturally incorporates local Lorentz symmetry and fermionic couplings while displaying a gauge-like structure. We argue that the coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of QG. The purpose of this work is not to provide a complete quantization of teleparallel gravity but to identify the geometric and conceptual ingredients that such a formulation would require. Full article
(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization, 2nd Edition)
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