1,714 research outputs found
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 (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 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,) as the quantum statistical system of N
quantum (statistical) variables (X) and one {\it Euclidean time} variable
(). Introducing paths (lines or hypersurfaces) in this space
(X,), 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 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
The Finiteness Requirement for Six-Dimensional Euclidean Einstein Gravity
The finiteness requirement for Euclidean Einstein gravity is shown to be so
stringent that only the flat metric is allowed. We examine counterterms in 4D
and 6D Ricci-flat manifolds from general invariance arguments.Comment: 15 pages, Introduction is improved, many figures(eps
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
Effective gauge field theory of the t-J model in the charge-spin separated state and its transport properties
We study the slave-boson t-J model of cuprates with high superconducting
transition temperatures, and derive its low-energy effective field theory for
the charge-spin separated state in a self-consistent manner. The phase degrees
of freedom of the mean field for hoppings of holons and spinons can be regarded
as a U(1) gauge field, . The charge-spin separation occurs below certain
temperature, , as a deconfinement phenomenon of the dynamics of
. Below certain temperature , the spin-gap
phase develops as the Higgs phase of the gauge-field dynamics, and
acquires a mass . The effective field theory near takes the
form of Ginzburg-Landau theory of a complex scalar field coupled with
, where represents d-wave pairings of spinons. Three
dimensionality of the system is crucial to realize a phase transition at
.
By using this field theory, we calculate the dc resistivity . At , is proportional to . At , it deviates
downward from the -linear behavior as . When the system is near (but not) two dimensional, due to the compactness
of the phase of the field , the exponent deviates from its
mean-field value 1/2 and becomes a nonuniversal quantity which depends on
temperature and doping. This significantly improves the comparison with the
experimental data
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