Application of quantum field theory in particle physics, gravity, condensed matter physics and cosmology

引力：2013年，我和我的学生J. Belletête发现，能量和动量的配置是可能的，它们的行为就像负质量的粒子。这些组态是具有宇宙学常数的爱因斯坦方程的某些奇异解的光滑变形。后来，我的学生S。Mbarek，我们证明了它们可以用完美流体的能量动量来获得。我现在和未来的工作是首先找到一个动力学模型，它可以支持静态解的负质量和宇宙学的这些配置的后果。 CP破坏和孤子：我们研究了一个有效的CP破坏模型，它可以用来描述B介子衰变为4个轻标量介子的过程。这对应于CP破坏的有效标量场相互作用。在最简单的这种有效理论中，我们发现了丰富的孤子和瞬子谱。拓扑解原则上会引起对CP破坏过程的非微扰修正。宇宙中CP破坏的起源是一个重要的开放性问题。 量子自旋系统：大自旋量子系统可以使用自旋相干态路径积分来分析。我们用这个路径积分计算了隧道效应。我们已经表明，高阶微扰理论可以有效地计算使用路径积分。最重要的结果，我们已经发现，对应于确定的基态的一个N网站，量子自旋链，所描述的Haldom。研究了Blume-Capel-Haldane-Ising模型，得到了孤子具有有限尺寸的有趣结果，并对Haldane猜想的未解问题提供了新的解释. 诱导假真空衰减：我们研究了拓扑孤子引起的诱导假真空衰减。这些孤子必须在其内部包含标量场的零点，即对称性未破缺的点。因此，如果存在一个可以产生这些拓扑孤子的非平凡真空结构，那么自发破缺的假真空自然是不稳定的。我们发现，当孤子是薄壁的，他们可以是经典稳定的，但量子力学亚稳态由于量子隧道效应。未来的工作将包括考虑引力修正。 任意子和维里展开：我们已经开发了一种方法来数值模拟晶格上的任意子。我们的方法允许一个简单的推广计算N个任意子的正则配分函数，因此维里系数。维里展开是否对任意子气体有用是一个悬而未决的问题。只有前几个系数已在理论上获得，它是不知道，如果状态方程承认一个有用的扩展维里系数。任意子可以用于模拟量子计算，这将产生重大影响。

Gravitation: In 2013, with my student J. Belletête, we discovered it was possible to have configurations of energy and momentum, which behaved like particles of negative mass. These configurations were smooth deformations of certain singular solutions of Einstein’s equations with cosmological constant. Subsequently, with my student S. Mbarek, we demonstrated that they could be obtained with the energy-momentum of a perfect fluid. My present and future work on the subject is first to find a dynamical model, which can support static solutions with negative mass and the consequence of these configurations for cosmology. CP-Violation and solitons: We have studied an effective model of CP-violation that could be used to describe the decay of B mesons to 4 lighter scalar mesons. This corresponds to an effective 5 scalar field interaction that is CP violating. In the simplest such effective theory, we find a rich spectrum of solitons and instantons. The topological solutions would in principle give rise to non-perturbative corrections to CP-violating processes. It is an open important problem to understand the source of CP violation in the universe. Quantum spin systems: Large spin quantum systems can be analyzed using the spin coherent state path integral. We have computed tunnelling with this path integral. We have shown that high orders in perturbation theory can be efficiently computed using the path integral. The most important result that we have found corresponds to identifying the ground state of an N site, quantum spin chain, described by Haldane. Studying the related Blume-Capel-Haldane-Ising model, we find the interesting result that the solitons have a finite size, and could shed light on the Haldane conjecture which is still an open problem. Induced, false vacuum decay: We have studied induced false vacuum decay due to topological solitons. These solitons must contain a zero of the scalar field in their interiors, a point where the symmetry is unbroken. Thus a spontaneously broken, false vacuum would naturally be unstable if there existed a non-trivial vacuum structure in which these topological solitons can arise. We show that when the solitons are thin walled, they can be classically stable, but quantum mechanically meta-stable due to quantum tunnelling. Future work will involve taking into account gravitational corrections. Anyons and the virial expansion: We have developed a method to numerically simulate anyons on the lattice. Our method allows for a simple generalization to computing the canonical partition function for N anyons, and hence the virial coefficients. It is an open problem if the virial expansion is useful for a gas of anyons. Only the first few coefficients have been accessed theoretically, and it is not known if the equation of state admits a useful expansion in the virial coefficients. Anyons could be used for simulating quantum computation which would have significant impact.