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

万有引力：2013年，我和我的学生J. Belletête一起发现有可能存在能量和动量的构型，它们表现得像负质量的粒子。这些构形是爱因斯坦带宇宙常数方程的某些奇异解的光滑变形。随后，我和我的学生S. Mbarek一起证明了它们可以用完美流体的能量动量得到。我现在和将来在这个问题上的工作首先是找到一个动态模型，它可以支持具有负质量的静态解以及这些配置对宇宙学的影响。*** cp -违和和孤子：我们研究了一个有效的cp -违和模型，可以用来描述B介子到4个更轻的标量介子的衰变。这对应于一个违反CP的有效5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。拓扑解原则上会对cp -违反过程产生非微扰修正。了解宇宙中CP破坏的来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进行分析。我们已经用这个路径积分计算了隧道效应。我们证明了用路径积分可以有效地计算摄动理论中的高阶。我们发现的最重要的结果对应于确定一个N位的基态，量子自旋链，由霍尔丹描述。通过研究相关的Blume-Capel-Haldane-Ising模型，我们发现了一个有趣的结果，即孤子的大小是有限的，这可能会对霍尔丹猜想这一尚未解决的问题有所启发。***诱导假真空衰减：我们已经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，即对称不被破坏的点。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，那么一个自发破缺的假真空自然是不稳定的。我们表明，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，它们可以是量子力学亚稳定的。未来的工作将包括考虑重力修正。***任意子和虚展开：我们开发了一种数值模拟晶格上任意子的方法。我们的方法允许一个简单的推广，以计算N个任意子的正则配分函数，从而计算维里系数。这是一个开放的问题，如果病毒膨胀是有用的气体的任意子。只有前几个系数已经在理论上得到了，而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。任意子都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. **