Chirality in Affine Spaces and in Spacetime

Abstract

An object is chiral when its symmetry group contains no indirect isometry. It can be difficult to classify isometries as direct or indirect, except in the Euclidean case. We classify them with the help of outer semidirect products of isometry groups, in particular in the case of an affine space defined over a finite-dimensional real quadratic space. We also classify as direct or indirect the isometries of the real Lorentz-Minkowski spacetime and those of the classical spacetime defined by the Newton-Cartan theory.

Fundamental Cause of Bio-Chirality - Space-Time Symmetry: Concept Review

“…The concept of chirality applies to objects of all known domains of space dimensions, including mega-and micro-scales. Lorentz symmetry group transformations reflect the fundamental symmetry of space and time, which are critical to many physical laws, equations, and theories, including the kinetic law of special relativity, Maxwell's equation for electromagnetism, Dirac equation for an electron, and the standard model (SM) of elementary particles (EPs) [Petitjean, 2019;Liu, et al, 2019;Petitjean, 2022;Anais & Pedro. 2019].…”