Lattice Field Theory and Hadronic Physics

夸克携带色荷，核物质是由胶子介导的色夸克结合形成的。量子色动力学（QCD）是描述这些色电荷相互作用的理论。实验表明夸克有三种颜色，但所有的核物质都是中性的。将核物质分离成夸克和胶子需要非常大的能量，类似于早期宇宙中存在的能量。由于用三种颜色求解QCD已被证明是非常困难的，而且由于定性性质不依赖于颜色的数量，因此我们尝试按照Hooft的方法求解大量颜色的QCD。在过去的六年里，利用晶格规范理论的研究在提取一些物理结果方面被证明是非常有用的。我们将继续取得进展，并将重点放在高密度（如中子星内部）和高温（接近大爆炸）下存在的理论阶段。数值计算将用于研究这一阶段的夸克物质，我们将尝试与RHIC和CERN目前的实验进行定性比较。由于大色数极限下的QCD与弦理论的最新发展密切相关，我们也将能够在场论和弦理论之间建立联系。我们已经证明了夸克形成了一种无色的凝聚体，我们还成功地计算出了最轻的无色粒子——介子的性质。作为这个提议的一部分，我们将尝试计算其他较重的无色粒子的质量。我们还将尝试研究温度的影响，从而为夸克和胶子的原始汤形成核物质提供证据。科学的方法包括解析计算和数值计算。在FIU攻读博士学位的研究生将学习量子场论和数值技术，并将做出重大贡献。计算机集群将用于数值计算，作为该提案的一部分获得的结果将在核物理和粒子物理的国际会议上发表。

Quarks carry a color charge and nuclear matter is formed from the binding of colored quarks mediated by gluons. Quantum Chromo-Dynamics (QCD) is the theory that describes the interaction of these color charges. Experiments have shown than quarks come in three colors but all nuclear matter is color neutral. Separation of nuclear matter into quarks and gluons needs very large energies similar to what was present in the early universe. Since solving QCD with three colors have proven to be very difficult and since qualitative properties do not depend on the number of colors, an attempt following 't Hooft is made to solve QCD for a very large number of colors. Research using lattice gauge theory has proven to be quite useful in extracting several physics results in the last six years. We will continue to make progress and focus on the phase of the theory that exists at high densities (like inside neutron stars) and high temperatures (close to the big-bang). Numerical computations will be used to study quark matter in this phase and we will attempt to make qualitative comparisons with current experiments in RHIC and CERN. Since QCD in the limit of large number of colors is closely related to recent developments in string theory we will also be able to make connections between field theory and string theory. We have already shown that quarks form a colorless condensate and we have also succeeded in computing the properties of the lightest colorless particle - the pion. We will attempt to compute the masses of other heavier colorless particles as part of this proposal. We will also attempt to study the effect of temperature thereby showing evidence for the formation of nuclear matter from a primordial soup of quarks and gluons.The scientific methods involve analytical calculations and numerical computations. A graduate student at FIU working toward a Ph.D will learn quantum field theory and numerical techniques and will make significant contributions. Computer clusters will be used for numerical computations and the results obtained as part of this proposal will be presented at international conferences in nuclear and particle physics.