Holographic coordinates

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Ulrych, S.¹ 

[1] Wehrenbachhalde 35, CH-8053 Zurich, Switzerland

关键词: Laplace equation;    Holographic principle;    Projective geometry;    Bicomplex numbers;    Clifford algebras;   

DOI  :  10.1016/j.jmaa.2018.05.055

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free