Mathematical Sciences: Conformal Field Theory and Its Generalizations

小行星9627782 拟议的研究在于数学物理的一般领域。在此之前，研究人员致力于二维量子场论，澄清量子上同调理论中代数结构的各个方面。研究人员计划进一步追求这一点，并纳入更多的几何方面，如镜像流形和卡-丘理论。另一个子计划是利用双圈上循环来处理量子场论的四维推广。最后，调查员打算考虑共形场论和理想流体力学之间可能的联系，通过几何学的同构群。 量子场论是在试图给出自然界基本力的统一表述的背景下产生的。这个理论的二维“共形”表述相对来说是很好理解的，至少从纯数学的角度来看是这样的，而目前的提议试图进一步研究二维模型，以期将弦理论应用于基本粒子的现象学。

9627782 Zuckerman The proposed research lies in the general area of mathematical physics. Previously, the investigator worked on two-dimensional quantum field theory, clarifying various aspects of the algebraic structure in quantum cohomology theory. The investigator plans to further pursue this, incorporating also the more geometric aspects such as mirror manifolds and Calabi-Yau theory. Another subproject deals with four-dimensional generalizations of quantum field theory using double loop cocycles. Finally, the investigator intends to consider possible links between conformal field theories and ideal hydrodynamics via the geometry of diffeomorphism groups. Quantum field theory arises in the context of attempting to give a unified formulation of basic forces of nature. Two-dimensional 'conformal' formulation of this theory is relatively well-understood, at least from a purely mathematical standpoint, and the present proposal seeks to further study the two-dimensional model with a view towards applying string theory to the phenomenology of elementary particles.