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

Quantum Dynamics of a Bulk-Boundary System

The quantum dynamics of a bulk-boundary theory is closely examined by the use of the background field method. As an example we take the Mirabelli-Peskin model, which is composed of 5D super Yang-Mills (bulk) and 4D Wess-Zumino (boundary). Singular interaction terms play an important role of canceling the divergences coming from the KK-mode sum. Some new regularization of the momentum integral is proposed. An interesting background configuration of scalar fields is found. It is a localized solution of the field equation. In this process of the vacuum search, we present a new treatment of the vacuum with respect to the extra coordinate. The "supersymmetric" effective potential is obtained at the 1-loop full (w.r.t. the coupling) level. This is the bulk-boundary generalization of the Coleman-Weinberg's case. Renormalization group analysis is done where the correct 4d result is reproduced. The Casimir energy is calculated and is compared with the case of the Kaluza-Klein model.Comment: 57 pages,10 figures, final version

Product formula related to quantum Zeno dynamics

We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection $P$ on a separable Hilbert space \HH, with the convergence in L^2_\mathrm{loc}(\mathbb{R};\HH). It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace \hbox{$\mathrm{Ran} P$}. The convergence in \HH is demonstrated in the case of a finite-dimensional $P$. The main result is illustrated in the example where the projection corresponds to a domain in $\mathbb{R}^d$ and the unitary group is the free Schr\"odinger evolution.Comment: LaTeX 2e, 24 pages, with substantial modifications, to appear in Ann. H. Poincar

Brane-Anti-Brane Solution and SUSY Effective Potential in Five Dimensional Mirabelli-Peskin Model

A localized configuration is found in the 5D bulk-boundary theory on an $S_1/Z_2$ orbifold model of Mirabelli-Peskin. A bulk scalar and the extra (fifth) component of the bulk vector constitute the configuration. \Ncal=1 SUSY is preserved. The effective potential of the SUSY theory is obtained using the background field method. The vacuum is treated in a general way by allowing its dependence on the extra coordinate. Taking into account the {\it supersymmetric boundary condition}, the 1-loop full potential is obtained. The scalar-loop contribution to the Casimir energy is also obtained. Especially we find a {\it new} type which depends on the brane configuration parameters besides the $S_1$ periodicity parameter.Comment: 14 pages, 4 figures, Some points are improve

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

Lattice Dirac fermions in a non-Abelian random gauge potential: Many flavors, chiral symmetry restoration and localization

In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed there that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall reexamine the multi-flavor or multi-species case rather in detail and argue that the correlator at the band center decays {\em exponentially} for the case of a {\em large} number of flavors. This means that a delocalization-localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studies on multi-flavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behaviour of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD.Comment: Version appears in Mod.Phys.Lett.A17(2002)135

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

Fluctuation effects of gauge fields in the slave-boson t-J model

We present a quantitative study of the charge-spin separation(CSS) phenomenon in a U(1) gauge theory of the t-J model of high-Tc superconductures. We calculate the critical temperature of confinement-deconfinement phase transition below which the CSS takes place.Comment: Latex, 9 pages, 3 figure