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

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

Wall and Anti-Wall in the Randall-Sundrum Model and A New Infrared Regularization

An approach to find the field equation solution of the Randall-Sundrum model with the $S^1/Z_2$ extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the {\it ends} of the extra compact axis, by taking a {\it new infrared regularization}. The stability is guaranteed from the outset by the kink boundary condition. A {\it continuous} (infrared-)regularized solution, which is a truncated {\it Fourier series} of a {\it discontinuous} solution, is utilized.The ultraviolet-infrared relation appears in the regularized solution.Comment: 36 pages, 29 eps figure file

Three Phases in the 3D Abelian Higgs Model with Nonlocal Gauge Interactions

We study the phase structure of the 3D nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by means of Monte-Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. We found that in contrast to the 3D local abelian Higgs model which has only one phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This result is quite important for studies on electron fractionalization phenomena in strongly-correlated electron systems. Implications to them are discussed

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

Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.Comment: 15 pages, 16 figure

Quasi-excitations and superconductivity in the t-J model on a ladder

We study the t-J model on a ladder by using slave-fermion-CP^1 formalism which is quite useful for study of lightly-doped high-T_c cuprates. By integrating half of spin variables, we obtain a low-energy effective field theory whose spin part is nothing but CP^1 sigma model. We especially focus on dynamics of composite gauge field which determines properties of quasi-excitations. Value of the coefficient of the topological term strongly influences gauge dynamics and explaines why properties of quasi-excitations depend on the number of legs of ladder. We also show that superconductivity appears as a result of short-range antiferromagnetism and order parameter has d-wave type symmetry.Comment: Latex, 28 pages and 1 figur

Bad expression influences time to androgen escape in prostate cancer

<b>OBJECTIVE</b>: To assess the role of selected downstream Bcl-2 family members (Bad, Bax, Bcl-2 and Bcl-xL) in the development of androgen-independent prostate cancer (AIPC), as androgen-deprivation therapy is the treatment of choice in advanced prostate cancer, yet patients generally relapse and progress to an AI state within 18–24 months. <b>PATIENTS, MATERIALS AND METHODS</b>: The patient cohort was established by retrospectively selecting patients with prostate cancer who had an initial response to androgen-deprivation therapy, but subsequently relapsed with AIPC. In all, 58 patients with prostate cancer were included with matched androgen-dependent (AD) and AI prostate tumours available for immunohistochemical analysis; two independent observers using a weighted-histoscore method scored the staining. Changes in Bad, Bax, Bcl-2 and Bcl-xL expression during transition to AIPC were evaluated and then correlated to known clinical variables. <b>RESULTS</b>: High Bad expression in AD tumours was associated with an increased time to biochemical relapse (<i>P</i> = 0.007) and a trend towards improved overall survival (<i>P</i> = 0.053). There were also trends towards a decrease in Bad (<i>P</i> = 0.068) and Bax (<i>P</i> = 0.055) expression with progression to AIPC. There were no significant results for Bcl-2 or Bcl-xL. <b>CONCLUSION</b>: There is evidence to suggest that Bad expression levels at diagnosis influence time to biochemical relapse and overall survival, and that levels of pro-apoptotic proteins Bad and Bax fall during AIPC development. Bad might therefore represent a possible positive prognostic marker and potential therapeutic target for AIPC in the future