Casimir Energy of the Universe and the Dark Energy Problem

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function (\be-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.Comment: 12 pages, 13 figures, Proceedings of DSU2011(2011.9.26-30,Beijin

Casimir Energy of the Universe and New Regularization of Higher Dimensional Quantum Field Theories

Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory in the {\it warped} geometry. It is compared with the flat case. A new regularization, called {\it sphere lattice regularization}, is taken. In the integration over the 5D space, we introduce two boundary curves (IR-surface and UV-surface) based on the {\it minimal area principle}. It is a {\it direct} realization of the geometrical approach to the {\it renormalization group}. The regularized configuration is {\it closed-string like}. We do {\it not} take the KK-expansion approach. Instead, the position/momentum propagator is exploited, combined with the {\it heat-kernel method}. All expressions are closed-form (not KK-expanded form). The {\it generalized} P/M propagators are introduced. We numerically evaluate \La(4D UV-cutoff), \om(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. We present two {\it new ideas} in order to define the 5D QFT: 1) the summation (integral) region over the 5D space is {\it restricted} by two minimal surfaces (IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and require the dominant contribution, in the summation, is given by the {\it minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} \om suffers from the {\it renormalization effect}. The IR parameter $T$ does not. We examine the meaning of the weight function and finally reach a {\it new definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are quantized} with the extra coordinate as the Euclidean time (inverse temperature). We examine the cosmological constant problem and present an answer at the end. Dirac's large number naturally appears.Comment: 13 paes, 8 figures, proceedings of 1st Mediterranean Conf. on CQ

Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\it Euclidean time} variable ($\tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$\tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\it mechanical} system. The system Hamiltonian appears as the {\it area}. We show quantization is realized by the {\it minimal area principle} in the present geometric approach. When we take a {\it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {\it hyper-surface} as the path, the system Hamiltonian is given by the {\it area} of the {\it hyper-surface} which is defined as a {\it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.Comment: 20 pages, 8 figures, Proceedings of ICFS2010 (2010.9.13-18, Ise-Shima, Mie, Japan

河川改修による一ノ瀬湿原の植生変動

The Ichinose Moor of the Shiga Heights，l ocated in tlle northeast part of Nagano Preffecture，had changed to the dry grassland，b y deep erosion of the stream at thecentral part of the moor. The trial was made to get upraising water level by setting artificia! weirs in the stream; A study has started to make surveys concerning to the effect of improved groundwater level on the change of the M、egetationat Ichinose Moor. The result of surveys in the early stage is reported here.Article環境科学年報16:47-52(1994)research repor

Gauge Theory of Composite Fermions: Particle-Flux Separation in Quantum Hall Systems

Fractionalization phenomenon of electrons in quantum Hall states is studied in terms of U(1) gauge theory. We focus on the Chern-Simons(CS) fermion description of the quantum Hall effect(QHE) at the filling factor $\nu=p/(2pq\pm 1)$, and show that the successful composite-fermions(CF) theory of Jain acquires a solid theoretical basis, which we call particle-flux separation(PFS). PFS can be studied efficiently by a gauge theory and characterized as a deconfinement phenomenon in the corresponding gauge dynamics. The PFS takes place at low temperatures, $T \leq T_{\rm PFS}$, where each electron or CS fermion splinters off into two quasiparticles, a fermionic chargeon and a bosonic fluxon. The chargeon is nothing but Jain's CF, and the fluxon carries $2q$ units of CS fluxes. At sufficiently low temperatures $T \leq T_{\rm BC} (< T_{\rm PFS})$, fluxons Bose-condense uniformly and (partly) cancel the external magnetic field, producing the correlation holes. This partial cancellation validates the mean-field theory in Jain's CF approach. FQHE takes place at $T < T_{\rm BC}$ as a joint effect of (i) integer QHE of chargeons under the residual field $\Delta B$ and (ii) Bose condensation of fluxons. We calculate the phase-transition temperature $T_{\rm PFS}$ and the CF mass. PFS is a counterpart of the charge-spin separation in the t-J model of high-$T_{\rm c}$ cuprates in which each electron dissociates into holon and spinon. Quasiexcitations and resistivity in the PFS state are also studied. The resistivity is just the sum of contributions of chargeons and fluxons, and $\rho_{xx}$ changes its behavior at $T = T_{\rm PFS}$, reflecting the change of quasiparticles from chargeons and fluxons at $T < T_{\rm PFS}$ to electrons at $T_{\rm PFS} < T$.Comment: 18 pages, 7 figure

Non-equilibrium Statistical Approach to Friction Models

A geometric approach to the friction phenomena is presented. It is based on the holographic view which has recently been popular in the theoretical physics community. We see the system in one-dimension-higher space. The heat-producing phenomena are most widely treated by using the non-equilibrium statistical physics. We take 2 models of the earthquake. The dissipative systems are here formulated from the geometric standpoint. The statistical fluctuation is taken into account by using the (generalized) Feynman's path-integral.Comment: 6 pages, 7 figure