Conformal Fluctuations of the Interior Schwarzschild Solution

The basic formalism for conformal fluctuations of the gravitational field is presented. After developing a master propagator for the interior Schwarzschild solution, the time development of the gravitational wave function is considered. The effect of the two classical singularities (resp. pseudo-singularities) of the Schwarzschild solution on the quantum wave function for the gravitational field is studied using a wave function initially localized on the classical solution. While the true singularity at r = 0 imparts consequences on the wave function that cannot be ignored, the pseudo-singularity at the event horizon does not seem to cause any divergences on the interior fluctuations of the Schwarzschild solution.     

STATISTICAL ENTROPIES OF THE TAUB－NUT/BOLT AdS SPACES FROM THE HORIZON CONFORMAL FIELD THEORY

The covariant phase technique is used to compute the constraint algebra of the four-dimensional space-times which are asymptotic to anti-de Sitter (AdS), such as the planar Taub－NUT AdS and Taub－bolt AdS spaces, and the hyperbolic Taub－bolt AdS space. The standard Virasoro subalgebrae with corresponding central charges for these objects are constructed and the resulting densities of states yield the expected Bekenstein－Hawking entropies.     

Strongly Extremal Kähler Metrics

On a compact complex manifold (M, J) of the Kähler type, we consider the functional defined by the L²-norm of the scalar curvature with its domain the space of Kähler metrics of fixed total volume. We calculate its critical points, and derive a formula that relates the Kähler and Ricci forms of such metrics on surfaces. If these metrics have a nonzero constant scalar curvature, then they must be Einstein. For surfaces, if the scalar curvature is nonconstant, these critical metrics are conformally equivalent to non-Kähler Einstein metrics on an open dense subset of the manifold. We also calculate the Hessian of the lower bound of the functional at a critical extremal class, and show that, in low dimensions, these classes are weakly stable minima for the said bound. We use this result to discuss some applications concerning the two-points blow-up of CP².     

Simple Conformal Superalgebras of Finite Growth

In this paper, we construct six families of infinite simple conformal superalgebras of finite growth based on our earlier work on constructing vertex operator superalgebras from graded assocaitive algebras. Three subfamilies of these conformal superalgebras are generated by simple Jordan algebras of types A, B, and C in a certain sense.Research supported by Hong Kong RGC Competitive Earmarked Research Grant HKUST709/96P.2000 Mathematics Subject Classification: primary 17A30, 17A60; secondary 17B20, 81Q60     

Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.     

一种用于多叶准直器适形放疗的剂量算法研究

描述了一种用于多叶准直器适形放疗的剂量计算方法。 在不同大小的方野和非规则野照射情况下, 将此方法得到的剂量分布与微分卷积法计算得到的剂量分布进行了精度验证。 结果表明, 这种算法具有较高的剂量精度和较快的计算速度, 因此可在适形放疗中用作MLC适形野的自动生成。 A dose calculation algorithm for MLC based conformal radiotherapy is described in this paper. The algorithm is formulated by the coordinate of MLC leaves. Verification on the algorithm is made by comparing the dose distributions generated by this algorithm with that generated by a Differential Convolution Superposition algorithm for various regular and irregular fields. The results demonstrate that the present algorithm has suitable accuracy and high computational efficiency, thus it could be useful for the treatment planning process in MLC based conformal radiotherapy, where the workload for interactively or automatically designing the shapes of MLC is heavy.     

Standard Tractors and the Conformal Ambient Metric Construction

In this paper we relate the Fefferman–Graham ambientmetric construction for conformal manifolds to the approach toconformal geometry via the canonical Cartan connection. We show thatfrom any ambient metric that satisfies a weakening of the usualnormalisation condition, one can construct the conformal standardtractor bundle and the normal standard tractor connection, which areequivalent to the Cartan bundle and the Cartan connection. This resultis applied to obtain a procedure to get tractor formulae for allconformal invariants that can be obtained from the ambient metricconstruction. We also get information on ambient metrics whichare Ricci flat to higher order than guaranteed by the results ofFefferman–Graham.     

Isothermal fluid sphere: Uniqueness and conformal mapping

We prove the theorem: A necessary and sufficient condition for a spacetime to represent an isothermal fluid sphere (linear equation of state with density falling off as inverse square of the curvature radius) without boundary is that it is conformal to a spacetime of zero gravitational mass (‘minimally’ curved).