The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-pa...The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.展开更多
In this paper, we address the spectra of simple harmonic oscillators based on the generalized uncertainty principle (GUP) with a Kaluza-Klein compactified extra dimension. We show that in this scenario, to make the re...In this paper, we address the spectra of simple harmonic oscillators based on the generalized uncertainty principle (GUP) with a Kaluza-Klein compactified extra dimension. We show that in this scenario, to make the results compatible with experiments, the minimal length scale equals to the radius of compact extra dimension.展开更多
文摘The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.
文摘In this paper, we address the spectra of simple harmonic oscillators based on the generalized uncertainty principle (GUP) with a Kaluza-Klein compactified extra dimension. We show that in this scenario, to make the results compatible with experiments, the minimal length scale equals to the radius of compact extra dimension.
