Geometric quantization rules in QCPB theory

Using the QCPB theory, we can accomplish the compatible combination of the quantum mechanics and general relativity supported by the G-dynamics. We further study the generalized quantum harmonic oscillator, such as geometric creation and annihilation operators, especially, the geometric quantization rules based on the QCPB theory.Comment: 14 page

Emergence of Space and Spacetime Dynamics of Friedmann-Robertson-Walker Universe

In a recent paper [arXiv:1206.4916] by T. Padmanabhan, it was argued that our universe provides an ideal setup to stress the issue that cosmic space is emergent as cosmic time progresses and that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this note following this proposal we obtain the Friedmann equation of a higher dimensional Friedmann-Robertson-Walker universe. By properly modifying the volume increase and the number of degrees of freedom on the holographic surface from the entropy formulas of black hole in the Gauss-Bonnet gravity and more general Lovelock gravity, we also get corresponding dynamical equations of the universe in those gravity theories.Comment: Latex 9 pages without figur

Dynamics and thermodynamics of a probe brane in the multicenter and rotating D3-brane background

We study the dynamics and thermodynamics of a probe D3-brane in the rotating D3-brane background and in its extremal limit, which is a multicenter configuration of D3-branes distributed uniformly on a disc. In the extremal background, if the angular momentum of the probe does not vanish, the probe is always bounced back at some turning point. When its angular momentum vanishes, in the disc plane, the probe will be captured at the edge of the disc; in the hyperplane orthogonal to the disc, the probe will be absorbed at the center of the disc. In the non-extremal background, if the probe is in the hyperplane orthogonal to the disc, it will be captured at the horizon; if the probe is restricted in the disc plane, the probe will be bounced back at a turning point, which is just the infinite red-shift hyperplane of the rotating background, even when the angular momentum of the probe vanishes. The thermodynamics of a relative static D3-brane probe is also investigated to the rotating D3-brane source. Two critical points are found. One is just the thermodynamically stable boundary of the source rotating D3-branes; the other is related to the distance between the probe and the source, which can be regarded as the mass scale in the corresponding super Yang-Mills theory. If the probe is static, the second critical point occurs as the probe is at the infinite red-shift hyperplane of the background. The relevance to the thermodynamics of the super Yang-Mills theory is discussed briefly.Comment: Revtex, 16 pages, no figures, minor change

Quantum Radion on de Sitter branes

The quantum fluctuation of the relative location of two (n-1)-dimensional de Sitter branes (i.e., of n spacetime dimensions) embedded in the (n+1)-dimensional anti-de Sitter bulk, which we shall call the quantum radion, is investigated at the linear perturbation level. The quantization of the radion is done by deriving the effective action of the radion. Assuming the positive tension brane is our universe, the effect of the quantum radion is evaluated by using the effective Einstein equations on the brane in which the radion contributes to the effective energy momentum tensor at the linear order of the radion amplitude. Specifically, the rms effective energy density arising from the quantum radion is compared with the background energy density. It is found out that this ratio remains small for reasonable values of the parameters of the model even without introducing a stabilizing mechanism for radion, although the radion itself has a negative mass squared and is unstable. The reason behind this phenomenon is also discussed.Comment: 17 pages, no figure