Special Issue "Symmetry and Geometry in Physics II"
Deadline for manuscript submissions: 31 January 2024 | Viewed by 11240
Interests: hyperbolic geometry; mathematical physics
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Nature organizes itself using the language of symmetry. In particular, the symmetry group of special relativity theory is the Lorentz transformation group SO (1,3). A physical system has Lorentz symmetry if the relevant laws of physics are invariant under Lorentz transformations. Lorentz symmetry is one of the cornerstones of modern physics. However, entangled particles involve Lorentz symmetry violation. Understanding entanglement in relativistic settings has been a key question in quantum mechanics. Remarkably, a plausible candidate for the symmetry group of the spacetime of a system of m n-dimensional entangled particles is the Lorentz group SO (m, n) of signature (m, n), for any m, n ∈ ℕ.
Lorentz groups involve relativistically admissible velocities governed by hyperbolic geometry and controlled by Einstein velocity addition. The resulting Einstein addition is a binary operation which is neither commutative nor associative. As such, it is a non-group gyrogroup operation that gives rise to gyrocommutative gyrogroups and gyrovector spaces. The latter, in turn, form the algebraic setting for hyperbolic geometry, just as vector spaces form the algebraic setting for Euclidean geometry.
Papers that study any of the following topics are welcome:
- Differential or hyperbolic geometry associated with Einstein addition;
- Einstein and Einstein-related gyrogroups and gyrovector spaces and their hyperbolic geometry;
- Quantum entanglement that involves Lorentz violation; and
- Physical applications of any Lorentz group SO (m, n) of signature (m, n), m, n > 1.
Prof. Dr. Abraham A. Ungar
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. Symmetry 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.
- Special relativity
- Lorentz symmetry group SO (1, 3)
- Lorentz symmetry groups SO (m, n), m, n > 1
- SO (m, n), m, n > 1, and quantum entanglement
- Lorentz symmetry violation in quantum entanglement
- hyperbolic geometry approach to Einstein addition
- differential geometry approach to Einstein addition
- Einstein gyrogroups
- Einstein gyrovector spaces