1,927 research outputs found
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
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
CP-Violation in Kaluza-Klein and Randall-Sundrum Theories
The Kaluza-Klein theory and Randall-Sundrum theory are examined
comparatively, with focus on the five dimensional (Dirac) fermion and the
dimensional reduction to four dimensions. They are treated in the Cartan
formalism. The chiral property, localization, anomaly phenomena are examined.
The electric and magnetic dipole moment terms naturally appear. The order
estimation of the couplings is done. This is a possible origin of the
CP-violation.Comment: 3 pages, 2 figures, Proceedings of the Fifth KEK Topical Conference
-Frontiers in Flavor Physics
Casimir Energy of 5D Electro-Magnetism and Sphere Lattice Regularization
Casimir energy is calculated in the 5D warped system. It is compared with the
flat one. The position/ momentum propagator is exploited. A new regularization,
called {\it sphere lattice regularization}, is introduced. It is a direct
realization of the geometrical interpretation of the renormalization group. The
regularized configuration is closed-string like. We do {\it not} take the
KK-expansion approach. Instead the P/M propagator is exploited, combined with
the heat-kernel method. All expressions are closed-form (not KK-expanded form).
Rigorous quantities are only treated (non-perturbative treatment). The properly
regularized form of Casimir energy, is expressed in the closed form. We
numerically evaluate its \La(4D UV-cutoff), \om(5D bulk curvature,
warpedness parameter) and (extra space IR parameter) dependence.Comment: 3 pages, 3 figures, Proceedings of WS "Prog. String th. and
QFT"(Osaka City Univ., 07.12.7-10
Weak Field Expansion of Gravity: Graphs, Matrices and Topology
We present some approaches to the perturbative analysis of the classical and
quantum gravity. First we introduce a graphical representation for a global
SO(n) tensor (\pl)^d h_\ab, which generally appears in the weak field
expansion around the flat space: g_\mn=\del_\mn+h_\mn. Making use of this
representation, we explain 1) Generating function of graphs (Feynman diagram
approach), 2) Adjacency matrix (Matrix approach), 3) Graphical classification
in terms of "topology indices" (Topology approach), 4) The Young tableau
(Symmetric group approach). We systematically construct the global SO(n)
invariants. How to show the independence and completeness of those invariants
is the main theme. We explain it taking simple examples of \pl\pl h-, {and}
(\pl\pl h)^2- invariants in the text. The results are applied to the analysis
of the independence of general invariants and (the leading order of) the Weyl
anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10
dimensions).Comment: 41pages, 26 figures, Latex, epsf.st
Thermodynamic Properties, Phases and Classical Vacua of Two Dimensional -Gravity
Two dimensional quantum R-gravity is formulated in the semiclassical
method. The thermodynamic properties,such as the equation of state, the
temperature and the entropy, are explained. The topology constraint and the
area constraint are properly taken into account. A total derivative term and an
infrared regularization play important roles. The classical solutions (vacua)
of R-Liouville equation are obtained by making use of the well-known
solution of the ordinary Liouville equation. The positive and negative constant
curvature solutions are 'dual' each other. Each solution has two
branches(). We characterize all phases. The topology of a sphere is mainly
considered.Comment: 32 pages, Figures are not include
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
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
- …