Holographic coordinates

Abstract

The Laplace equation in the two-dimensional Euclidean plane is considered in the context of the inverse stereographic projection. The Lie algebra of the conformal group as the symmetry group of the Laplace equation can be represented solely in terms of the solutions and derivatives of the solutions of the Laplace equation. It is then possible to put contents from differential geometry and quantum systems, like the Hopf bundle, relativistic spin, bicomplex numbers, and the Fock space into a common context. The basis elements of the complex numbers, considered as a Clifford paravector algebra, are reinterpreted as differential tangent vectors referring to dilations and rotations. In relation to this a homogeneous space is defined with the Lie algebra of the conformal group, where dilations and rotations are the coset representatives. Potential applications in physics are discussed.

References in corpus (15)

• Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
• Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
• Quantum critical transport, duality, and M-theory
• More on Supersymmetric and 2d Analogs of the SYK Model
• Light-Front Higher-Spin Theories in Flat Space
• Skyrmions, instantons and holography
• States of Carbon-12 in the Skyrme Model
• Higher-Spin Algebras, Holography and Flat Space
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• Classically isospinning Skyrmion solutions
• Scattering of Skyrmions
• Two-Dimensional Conformal Models of Space-Time and Their Compactification
• Geometric Models of Helium
• Conformal numbers