69,813 research outputs found
Improved Perturbation Method and its Application to the IIB Matrix Model
We present a new scheme for extracting approximate values in ``the improved
perturbation method'', which is a sort of resummation technique capable of
evaluating a series outside the radius of convergence. We employ the
distribution profile of the series that is weighted by nth-order derivatives
with respect to the artificially introduced parameters. By those weightings the
distribution becomes more sensitive to the ``plateau'' structure in which the
consistency condition of the method is satisfied. The scheme works effectively
even in such cases that the system involves many parameters. We also propose
that this scheme has to be applied to each observables separately and be
analyzed comprehensively.
We apply this scheme to the analysis of the IIB matrix model by the improved
perturbation method obtained up to eighth order of perturbation in the former
works. We consider here the possibility of spontaneous breakdown of Lorentz
symmetry, and evaluate the free energy and the anisotropy of space-time extent.
In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-
and SO(7)-symmetric vacua that have been observed. It is also found that there
are two distinct SO(4)-symmetric vacua that have almost the same value of free
energy but the extent of space-time is different. From the approximate values
of free energy, we conclude that the SO(4)-symmetric vacua are most preferred
among those three types of vacua.Comment: 52 pages, published versio
On the Definition of the Partition Function in Quantum Regge Calculus
We argue that the definition of the partition function used recently to
demonstrate the failure of Regge calculus is wrong. In fact, in the
one-dimensional case, we show that there is a more natural definition, with
which one can reproduce the correct results.Comment: 9 pages, LaTe
A Failing Grade: "High-Tuition/High-Aid"
In the face of impending budget cuts to higher education, Washington policymakers are considering adopting a "high-tuition/high-aid" model that significantly increases tuition, partly offset with more financial aid. The assumption of this approach is that students who can afford it pay more; those students who cannot, benefit from larger financial aid packages. But the experience of universities that have adopted this model shows that high-tuition/high-aid preserves neither access nor quality
Differential Geometry of Microlinear Frolicher Spaces II
In this paper, as the second in our series of papers on differential geometry
of microlinear Frolicher spaces, we study differenital forms. The principal
result is that the exterior differentiation is uniquely determined
geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely
determined geometrically or physically in classical vector calculus. This
infinitesimal characterization of exterior differentiation has been completely
missing in orthodox differential geometry
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