标题： 二维量子引力中的虚拟黑洞 显示英文标题

标题： The virtual black hole in 2d quantum gravity

摘要： 如最近所展示的（W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544, 403 (1999）），二维量子引力理论——包括球面约化的爱因斯坦引力——在其几何部分经过精确路径积分后，可以对（标量）物质的圈图进行微扰处理。显然，黑洞形成的经典机制应该包含在该理论的树近似中。这通过两个标量散射并通过其有效黑洞质量被识别为“虚拟黑洞”的中间态来证明是成立的。 当前讨论局限于无质量和有质量的最小耦合标量。在第一种情况下，概率幅发散，除非黑洞通过适当的边界条件“封堵”。对于有质量的标量，得到了有限的S矩阵元。 显示英文摘要

摘要： As shown recently (W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544, 403 (1999)) 2d quantum gravity theories --- including spherically reduced Einstein-gravity --- after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a ``virtual black hole''. The present discussion is restricted to minimally coupled scalars without and with mass. In the first case the probability amplitude diverges, except the black hole is ``plugged'' by a suitable boundary condition. For massive scalars a finite S-matrix element is obtained.