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

万有引力：2013年，我们和我的学生J·贝莱特发现，能量和动量的构型是可能的，它们的行为就像负质量的粒子。这些构型是具有宇宙常数的爱因斯坦方程某些奇异解的光滑变形。随后，我们和我的学生S·姆巴雷克一起，证明了它们可以通过完美流体的能量动量来获得。我目前和未来在这个问题上的工作是首先找到一个动力学模型，它可以支持负质量的静态解以及这些构型对宇宙学的影响。*CP破坏与孤子：我们研究了一个有效的CP破坏模型，该模型可以用来描述B介子到4个较轻标量介子的衰变。这对应于有效的5标量场相互作用，这违反了CP。在最简单的有效理论中，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。了解宇宙CP破坏的来源是一个悬而未决的重要问题。*量子自旋系统：大自旋量子系统可以用自旋相干态路径积分来分析。我们已经用这个路径积分计算了隧道效应。我们已经证明，利用路径积分可以有效地计算微扰理论中的高阶。我们发现的最重要的结果对应于确定霍尔丹所描述的N位量子自旋链的基态。通过对相关的Blume-Capel-Haldane-Ising模型的研究，我们发现了一个有趣的结果，即孤子的大小是有限的，并且可以解释仍然是一个开放问题的Haldane猜想。*诱导的伪真空衰变：我们研究了拓扑孤子引起的伪真空衰变。这些孤子的内部必须包含标量场的零点，在这一点上对称性是不会被破坏的。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，自发破裂的假真空自然是不稳定的。我们发现，当孤子是薄壁时，它们可以是经典稳定的，但由于量子隧道效应，它们在量子力学上是亚稳定的。未来的工作将包括考虑引力修正。*任意子和维里展开：我们发展了一种方法来数值模拟晶格上的任意子。我们的方法允许简单地推广到计算N个任意子的正则配分函数，从而计算维里系数。维里展开对于任意子气体是否有用，这是一个悬而未决的问题。从理论上讲，只有最初的几个系数被获得，并且不知道状态方程是否允许在维里系数中进行有用的展开。任意子可以用来模拟量子计算，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. **