U.S. - Uruguay Cooperative Research: Knot Theory and the Dynamics of Quantum Gravity

这个美洲项目奖将支持宾夕法尼亚州立大学的Jorge Pullin博士和乌拉圭蒙得维的亚共和国大学的Rodolfo Gambini博士之间关于量子引力的合作研究项目。这项研究将使用连接和循环技术来处理广义相对论的非微扰量子化。特别是，他们希望通过使用回路导数来探索哈密顿约束的定义，并找到将被所有约束湮灭的理论的物理态。这项研究要解决的一个重要问题是宇宙常数在理论的态空间中所起的作用。到目前为止，他们已经发现，具有宇宙常数的状态是依赖于框架的纽结不变量，而没有宇宙常数的状态是框架无关的。这是一种普通的行为，还是仅限于某些状态，将被调查。两组人对这一问题的态度是互补的。该方法结合了宾夕法尼亚州立大学研究人员的广义相对论和引力物理背景，以及蒙得维的亚小组在粒子物理方面的专业知识。***

9811610PullinThis Americas Program award will support a collaborative research project on quantum gravity between Dr. Jorge Pullin, the Pennsylvania State University and Dr. Rodolfo Gambini, Universidad de la Republica, Montevideo, Uruguay. The research will deal with nonperturbative quantization of general relativity using connection and loop techniques. In particular, they wish to explore the definition of a Hamiltonian constraint in terms of the use of the loop derivative, and find physical states for the theory that would be annihilated by all constraints.An important question to be addressed by this study is the role that the cosmological constant plays in the space of states of the theory. Up to now, they have found that states with a cosmological constant are framing-dependent knot invariants, whereas states without a cosmological constant are framing-independent. Whether this is a generic behavior or is confined to certain states only, will be investigated.The approach of both groups to the subject is complementary. The approach combines the background in general relativity and gravitational physics of the researchers at Penn State with the expertise of the Montevideo group in particle physics. ***