2004/12/08 by Zhi-Ming Gu, Gu, Zhi-Ming
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0412021
7 pages, 2 figures
arxiv created 2004/12/08 · openalex publication_date 2004/12/08 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The η-ξ space-time is suggested by Gui for the quantum field theory in 1988. This paper consists of two parts. The first part is devoted to the discussion of the global properties of the η-ξ space-time. The result contains a proof which asserts that the η-ξ space-time is homeomorphic to ℂ*× ℂ*× ℂ2 by means of two explicit maps, which shows that the η-ξ space-time allows a Lie group structure. Thus some transformation groups, one of which is isomorphic to the Lorentz group in two dimensions, can be found. The other part of the paper is the discussion about the embedding of some subspaces in the η-ξ space-time. In particular, it is pointed out that the Euclidean space-time and the Minkowskian space-time are linked in a way in the η-ξ space-time such that the tilde field appears naturally. In addition some formulae in the η-ξ space-time reappear in a more natural way.