Compactified Minkowski Space: Myths and Facts
Arkadiusz Jadczyk

TL;DR
This paper clarifies the mathematical structure of compactified Minkowski space, emphasizing its conformal symmetry, and introduces Clifford algebra tools and the Hodge star operator to resolve misconceptions.
Contribution
It presents two clear constructions of compactified Minkowski space based on Penrose's ideas, highlighting subtle mathematical points and connecting to Clifford algebra techniques.
Findings
Clarifies the structure of compactified Minkowski space.
Introduces the antilinear Hodge star operator in this context.
Relates the constructions to Clifford algebra and conformal symmetry.
Abstract
Minkowski space, conformal group, compactification, conformal infinity, conformal inversion, light cone at infinity, SU(2,2), SO(4,2), Hodge star operator, Clifford algebra, spinors, twistors, antilinear operators, exterior algebra, bivectors, isotropic subspaces, null geodesics, Lie spheres, Dupin cyclides, gravitation} \abstract{Maxwell's equations are invariant not only under the Lorentz group but also under the conformal group. Irving E. Segal has shown that while the Galilei group is a deformation of the Poincar\'e group, and the Poincar\'e group is a deformation of the conformal group, the conformal group ends the road, it is {\em rigid\}. There are thus compelling mathematical and physical reasons for promoting the conformal group to the role of the fundamental symmetry of space--time, more important than the Poincar\'e group that formed the group-theoretical basis of special and…
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Taxonomy
TopicsRelativity and Gravitational Theory · Cosmology and Gravitation Theories · Algebraic and Geometric Analysis
