1,361 research outputs found
New Approach to Cosmological Fluctuation using the Background Field Method and CMB Power Spectrum
A new field theory formulation is presented for the analysis of the CMB power
spectrum distribution in the cosmology. The background-field formalism is fully
used. Stimulated by the recent idea of the {\it emergent} gravity, the
gravitational (metric) field g_\mn is not taken as the quantum-field, but as
the background field. The statistical fluctuation effect of the metric field is
taken into account by the path (hyper-surface)-integral over the space-time.
Using a simple scalar model on the curved (dS) space-time, we explain the
above things with the following additional points: 1) Clear separate treatment
of the classical effect, the statistical effect and the quantum effect; 2) The
cosmological fluctuation comes not from the 'quantum' gravity but from the
unkown 'microscopic' movement; 3) IR parameter () is introduced for the
time axis as the periodicity. Time reversal(Z)-symmetry is introduced in
order to treat the problem separately with respect to the Z parity. This
procedure much helps both UV and IR regularization to work well.Comment: 6 pages, 5 figures, Presentation at
APPC12(Makuhari,Chiba,Japan,2013.7.14-19), JPS Conference Proceedings (in
press
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
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
, 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, , 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 units of CS fluxes. At sufficiently low temperatures , 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 as a joint effect of (i) integer QHE of
chargeons under the residual field and (ii) Bose condensation of
fluxons. We calculate the phase-transition temperature and the CF
mass. PFS is a counterpart of the charge-spin separation in the t-J model of
high- 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
changes its behavior at , reflecting the change of
quasiparticles from chargeons and fluxons at to electrons at
.Comment: 18 pages, 7 figure
Some Properties of Domain Wall Solution in the Randall-Sundrum Model
Properties of the domain wall (kink) solution in the 5 dimensional
Randall-Sundrum model are examined both {\it analytically} and {\it
numerically}. The configuration is derived by the bulk Higgs mechanism. We
focus on 1) the convergence property of the solution, 2) the stableness of the
solution, 3) the non-singular property of the Riemann curvature, 4) the
behaviours of the warp factor and the Higgs field. It is found that the bulk
curvature changes the sign around the surface of the wall. We also present some
{\it exact} solutions for two simple cases: a) the no potential case, b) the
cosmological term dominated case. Both solutions have the (naked) curvature
singularity. We can regard the domain wall solution as a singularity resolution
of the exact solutions.Comment: Typographical error correction for publication. 16 pages, 4 figure
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
CP Violation from a Higher Dimensional Model
It is shown that Randall-Sundrum model has the EDM term which violates the
CP-symmetry. The comparison with the case of Kaluza-Klein theory is done. The
chiral property, localization, anomaly phenomena are examined. We evaluate the
bulk quantum effect using the method of the induced effective action. This is a
new origin of the CP-violation.Comment: 15pages, Proc. of Int. Workshop on "Neutrino Masses and
Mixings"(Dec.17-19,2006,Univ.of Shizuoka,Japan
Conformal Anomaly in 4D Gravity-Matter Theories Non-minimally Coupled with Dilaton
The conformal anomaly for 4D gravity-matter theories, which are non-minimally
coupled with the dilaton, is systematically studied. Special care is taken for:
rescaling of fields, treatment of total derivatives, hermiticity of the system
operator and choice of measure. Scalar, spinor and vector fields are taken as
the matter quantum fields and their explicit conformal anomalies in the
gravity-dilaton background are found. The cohomology analysis is done and some
new conformal invariants and trivial terms, involving the dilaton, are
obtained. The symmetry of the constant shift of the dilaton field plays an
important role. The general structure of the conformal anomaly is examined. It
is shown that the dilaton affects the conformal anomaly characteristically for
each case: 1)[Scalar] The dilaton changes the conformal anomaly only by a new
conformal invariant, ; 2)[Spinor] The dilaton does {\it not} change the
conformal anomaly; 3)[Vector] The dilaton changes the conformal anomaly by
three new (generalized) conformal invariants, . We present some
new anomaly formulae which are useful for practical calculations. Finally, the
anomaly induced action is calculated for the dilatonic Wess-Zumino model. We
point out that the coefficient of the total derivative term in the conformal
anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the
disagreement between calculations in refs.\cite{ENO,NO,SI97,KLV} and the result
of Hawking-Bousso\cite{BH}.Comment: 37 pages, Latex, No figur
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
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