arXiv 0810.24192008-10-14hep-lat

格点量子场论的一种新计算方法

A new computational approach to lattice quantum field theories

Shailesh Chandrasekharan

备注：: 15 pages, 6 figures; Plenary talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA
发表信息：: PoS LATTICE2008:003,2008

摘要：

在过去的十年中，算法的发展表明，有一个新的计算方法，一类量子场论。该方法基于以类似于世界线表示的表示重写配分函数，因此我们将其称为“WL方法”。在参数空间的某些区域，这种方法可能比传统方法更强大，特别是在存在化学势或无质量费米子的情况下。虽然世界线表示在哈密顿公式中是自然的，但它们也可以直接在欧几里得空间中构造。我们首先描述的方法和它的优点，考虑经典的XY模型中存在的化学势。然后，我们认为，$CP^{N-1}$模型，模型的π介子的晶格和晶格无质量的Thirring模型，都可以制定和解决使用WL的方法。特别是，我们发现，WL-方法的Thirring模型导致一种新的行列式蒙特卡罗算法，我们称之为“动态袋”算法。最后，我们认为，一个简单的扩展的WL-方法规范理论导致一个世界片，“WS-方法”，在阿贝尔格点规范理论。

英文摘要：

Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the world-line representation and hence we shall call it the "WL-approach". This approach is likely to be more powerful than the conventional approach in some regions of parameter space, especially in the presence of chemical potentials or massless fermions. While world-line representations are natural in the Hamiltonian formulation, they can also be constructed directly in Euclidean space. We first describe the approach and its advantages by considering the classical XY model in the presence of a chemical potential. We then argue that, $CP^{N-1}$ models, models of pions on the lattice and the lattice massless Thirring model, can all be formulated and solved using the WL-approach. In particular, we discover that the WL-approach to the Thirring model leads to a novel determinantal Monte-Carlo algorithm which we call the "dynamical-bag" algorithm. Finally, we argue that a simple extension of the WL-approach to gauge theories leads to a world-sheet, "WS-approach", in Abelian Lattice Gauge theory.

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