Von Neumann Geometry and E(∞) Quantum Spacetime

✍ Scribed by M.S.El Naschie

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 621 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00186-6

✦ Synopsis

In this paper\ it is shown that von Neumann continuous geometry may be regarded as the _rst attempt towards formulating a general quantum spacetime geometry akin to that of Cantorian spacetime E " # and noncommutative geometry[ Þ 0887 Elsevier Science Ltd[ All rights reserved[ Notation E " # The complete in_nite dimensional hierarchical Cantorian spacetime[ E "n# An n dimensional subspace of E " # [ E "9# The zero dimensional Cantorian spacetime[ S "9# c The Kernel or null set of E " # [ d "9# c dim H S "9# c The Hausdor} dimension S "9# c [ d "0# c 0 The Hausdor} dimension of the normality set[ n Number of the topological dimensions or the formal dimension of E "n# [ d "n# c The Hausdor} dimension of an n dimensional Cantor set[ d "n# c "0:d "9# c # n-0 The bijection formula connecting d "n# c to d "9# c [ The Expectation value or the e}ective topological dimension of E " # ½ðnŁ ðdim T E " # Ł