English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Half of the Bondi-Metzner-Sachs (BMS) transformations consist oforientation-preserving conformal homeomorphisms of the extended complex planeknown as fractional linear (or Mobius) transformations. These can be of 4kinds, i.e. they are classified as being parabolic, or hyperbolic, or elliptic,or loxodromic, depending on the number of fixed points and on the value of thetrace of the associated 2x2 matrix in the projective version of the SL(2,C)group. The resulting particular forms of SL(2,C) matrices affect also the otherhalf of BMS transformations, and are used here to propose 4 realizations of theasymptotic symmetry group that we call, again, parabolic, or hyperbolic, orelliptic, or loxodromic. In the second part of the paper, we prove that asubset of hyperbolic and loxodromic transformations, those having trace thatapproaches infinity, correspond to the fulfillment of limit-point condition forsingular Sturm-Liouville problems. Thus, a profound link may exist between thelanguage for describing asymptotically flat space-times and the world ofcomplex analysis and self-adjoint problems in ordinary quantum mechanics.

From parabolic to loxodromic BMS transformations