U.S.-Brazil Cooperative Research on Quantum Field Theory

该奖项支持波士顿大学的Tadeusz Balaban和巴西米纳斯吉拉斯州联邦大学物理系的Ricardo Schor和Michael O'Carroll在应用数学方面的合作研究。问题是三维自旋量子电动力学的紫外稳定性以及重整化群方法在低温经典自旋模型（如海森堡模型）中的应用。这些研究人员一直在研究自由晶格电磁场的小扰动模型的红外特性和自旋电动力学的重整化群方法。在第一种情况下，他们证明了这些模型的红外渐近自由，并在最近发表了结果。对于第二个问题，旋量电动力学的二维模型是众所周知的，但三维模型是一个困难得多的问题。他们已经开始使用重整化群方法研究后一种情况。该奖项将支持这项新工作，该工作将首先对二维经典自旋模型进行紫外线稳定性研究，然后在修改后对三维情况进行研究，从而扩展成功和富有成效的初步合作。

This award supports cooperative research in applied mathematics to be conducted by Tadeusz Balaban of Boston University and Ricardo Schor and Michael O'Carroll of the physics department of the Federal University of Minas Gerais in Belo Horizonte, Brazil. The problem is the ultraviolet stability of three- dimensional spinor quantum electrodynamics and the application of renormalization group methods to low temperature classical spin models, such as the Heisenberg model. These researchers have been working on infrared properties of small perturbation models of the free lattice electromagnetic field and a renormalization group approach to spinor electrodynamics. In the first case they have proved the infrared asymptotic freedom for these models and have recently published the results. For the second problem, the two-dimensional model of spinor electrodynamics is well known but the three- dimensional model is a much more difficult problem. They have started work on the latter case using the renormalization group approach. This award will support this new work in which the ultraviolet stability will be investigated, first for two-dimensional classical spin models and then, after modifications, for the three-dimensional case thus extending a successful and productive preliminary collaboration.