# Symmetry and Geometry in Physics

A special issue of *Symmetry* (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: **closed (30 September 2021)** | Viewed by 33497

## Special Issue Editor

**Interests:**hyperbolic geometry; mathematical physics

Special Issues, Collections and Topics in MDPI journals

## Special Issue Information

Dear Colleagues,

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. Abraham A. Ungar*Guest Editor*

**Manuscript Submission Information**

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## Keywords

- 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

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