15,985 research outputs found
The Beltrami Model of De Sitter Space: From Snyder's quantized space-time to de Sitter invariant relativity
In terms of the Beltrami model of de Sitter space we show that there is an
interchangeable relation between Snyder's quantized space-time model in
dS-space of momenta at the Planck length and the
dS-invariant special relativity in dS-spacetime of radius
, which is another fundamental length related to
the cosmological constant. Here, the cosmological constant is
regarded as a fundamental constant together with the speed of light , Newton
constant and Planck constant . Furthermore, the physics at two
fundamental scales of length, the \dS-radius and the Planck length
, should be dual to each other and linked via the gravity with local
dS-invariance characterized by a dimensionless coupling constant .Comment: 15 pages. Invited talk given at `International workshop on
noncommutative geometry and physics', Beijing, Nov. 7-10, 2005. To appear in
the proceeding
Spin Mixing in Spinor Fermi Gases
We study a spinor fermionic system under the effect of spin-exchange
interaction. We focus on the interplay between the spin-exchange interaction
and the effective quadratic Zeeman shift. We examine the static and the dynamic
properties of both two- and many-body system. We find that the spin-exchange
interaction induces coherent Rabi oscillation in the two-body system, but the
oscillation is quickly damped when the system is extended to the many-body
case
Mean-variance portfolio selection under Volterra Heston model
Motivated by empirical evidence for rough volatility models, this paper
investigates continuous-time mean-variance (MV) portfolio selection under the
Volterra Heston model. Due to the non-Markovian and non-semimartingale nature
of the model, classic stochastic optimal control frameworks are not directly
applicable to the associated optimization problem. By constructing an auxiliary
stochastic process, we obtain the optimal investment strategy, which depends on
the solution to a Riccati-Volterra equation. The MV efficient frontier is shown
to maintain a quadratic curve. Numerical studies show that both roughness and
volatility of volatility materially affect the optimal strategy.Comment: Final version, 22 pages, 5 figures, to appear in Applied Mathematics
& Optimizatio
A Mixed-Binary Convex Quadratic Reformulation for Box-Constrained Nonconvex Quadratic Integer Program
In this paper, we propose a mixed-binary convex quadratic programming
reformulation for the box-constrained nonconvex quadratic integer program and
then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational
results demonstrate that our approach clearly outperform the very recent
state-of-the-art solvers.Comment: 8page
Conformal Triality of de Sitter, Minkowski and Anti-de Sitter Spaces
We describe how conformal Minkowski, dS- and AdS-spaces can be united into a
single submanifold [N] of RP^5. It is the set of generators of the null cone in
M^{2,4}. Conformal transformations on the Mink-, dS- and AdS-spaces are induced
by O(2,4) linear transformations on M^{2,4}. We also describe how Weyl
transformations and conformal transformations can be resulted in on [N]. In
such a picture we give a description of how the conformal Mink-, dS- and
AdS-spaces as well as [N] are mapped from one to another by conformal maps.
This implies that a CFT in one space can be translated into a CFT in another.
As a consequence, the AdS/CFT-correspondence should be extended.Comment: Talk on the XXIII International Conference of Differential Geometric
Methods in Theoretical Physics, Chern Institute of Mathematics (former Nankai
Institute of Mathematics), August 20--26, 2005. To appear in the proceedings,
published by World Scientific. Plain LaTeX, 10 pages, no figure
A comparison theorem for the law of large numbers in Banach spaces
Let be a real separable Banach space. Let be a sequence of i.i.d. {\bf B}-valued random variables and
set . Let and
be increasing sequences of positive real numbers such
that and is a nondecreasing sequence. In this paper, we provide a
comparison theorem for the law of large numbers for i.i.d. {\bf B}-valued
random variables. That is, we show that almost
surely (resp. in probability) for every {\bf B}-valued random variable with
(resp. ) if almost surely (resp. in probability) for every symmetric {\bf B}-valued
random variable with (resp. ). To
establish this comparison theorem for the law of large numbers, we invoke two
tools: 1) a comparison theorem for sums of independent {\bf B}-valued random
variables and, 2) a symmetrization procedure for the law of large numbers for
sums of independent {\bf B}-valued random variables. A few consequences of our
main results are provided.Comment: 19 page
Merton's portfolio problem under Volterra Heston model
This paper investigates Merton's portfolio problem in a rough stochastic
environment described by Volterra Heston model. The model has a non-Markovian
and non-semimartingale structure. By considering an auxiliary random process,
we solve the portfolio optimization problem with the martingale optimality
principle. Optimal strategies for power and exponential utilities are derived
in semi-closed form solutions depending on the respective Riccati-Volterra
equations. We numerically examine the relationship between investment demand
and volatility roughness.Comment: 14 pages, 3 figures, exponential utility adde
Intrinsic Vertex Regularization and Renormalization in Field Theory
Based upon the intrinsic relation between the divergent lower point functions
and the convergent higher point ones in the renormalizable quantum field
theories, we propose a new method for regularization and renormalization in
QFT. As an example, we renormalize the theory at the one loop order
by means of this method.Comment: 7p, 4figures not include
A new single-dynamical-scalar-field model of dark energy
A new single-dynamical-scalar-field model of dark energy is proposed, in
which either higher derivative terms nor structures of extra dimension are
needed. With the help of a fixed background vector field, the parameter for the
effective equation of state of dark energy may cross in the evolution of
the universe. After suitable choice of the potential, the crossing and
transition from decelerating to accelerating occur at and
, respectively.Comment: 7 pages, 4 figure
Principle of Relativity, Dual Poincar\'e Group and Relativistic Quadruple
Based on the principle of relativity with two universal constants (c, l) and
in the inertial motion group IM(1,3)\sim PGL(5,R), with Lorentz isotropy, in
addition to Poincar\'e group of Einstein's SR the dual Poincar\'e group
preserves the origin lightcone and its space/time-like region R_\pm appeared at
common origin of intersected Minkowski/dS/AdS space. The dual Poincare
kinematics is on a pair of degenerate Einstein manifolds with
\Lambda_\pm=\pm3l^{-2} for R_\pm, respectively. Thus, there is a Poincar\'e
double and the dS double for dS/AdS SR. Further, with other four doubles they
form a relativistic quadruple for three kinds of SR on M/D_\pm, respectively.
The dS SR with the dS-dual Poincare double provides new kinematics for cosmic
scale physics.Comment: 16 pages. Extended versio
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