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

量子场论在粒子物理、引力、凝聚态物理和宇宙学中的应用

• 批准号: SAPIN-2016-00035
• 负责人: Paranjape, Manu
• 金额: $ 1.82万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=661522
• 关键词: Application; quantum; field; theory; particle

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. **

万有引力：2013 年，我们和我的学生 J. Belletête 发现，能量和动量的构型是可能的，其行为就像负质量的粒子一样。这些配置是具有宇宙学常数的爱因斯坦方程的某些奇异解的平滑变形。 随后，我们与我的学生 S. Mbarek 一起证明了可以通过完美流体的能量动量来获得它们。我目前和未来在该主题上的工作首先是找到一个动力学模型，该模型可以支持具有负质量的静态解决方案以及这些配置对宇宙学的影响。 ***CP 破坏和孤子：我们研究了一种有效的 CP 破坏模型，可用于描述 B 介子到 4 个较轻标量介子的衰变。这对应于 CP 破坏的有效 5 标量场相互作用。在最简单的有效理论中，我们发现了丰富的孤子和瞬子谱。拓扑解决方案原则上会对 CP 破坏过程产生非微扰校正。了解宇宙中CP破坏的根源是一个悬而未决的重要问题。 ***量子自旋系统：可以使用自旋相干态路径积分来分析大型自旋量子系统。我们用这个路径积分计算了隧道效应。我们已经证明，可以使用路径积分有效地计算扰动理论中的高阶。我们发现的最重要的结果对应于识别霍尔丹描述的 N 位点（量子自旋链）的基态。 研究相关的 Blume-Capel-Haldane-Ising 模型，我们发现了一个有趣的结果，即孤子具有有限的尺寸，并且可以为霍尔丹猜想提供线索，这仍然是一个悬而未决的问题。***诱导假真空衰变：我们研究了拓扑孤子引起的诱导假真空衰变。 这些孤子的内部必须包含标量场的零，即对称性未破缺的点。因此，如果存在一个非平凡的真空结构，其中可以出现这些拓扑孤子，那么自发破裂的假真空自然会不稳定。我们证明，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而具有量子力学亚稳定。未来的工作将涉及考虑重力修正。 ***任意子和维里展开：我们开发了一种对晶格上的任意子进行数值模拟的方法。我们的方法允许简单地推广计算 N 个任意子的规范配分函数，从而计算维里系数。维里展开式对于任意子气体是否有用，这是一个悬而未决的问题。理论上只访问了前几个系数，并且不知道状态方程是否允许维里系数的有用扩展。任意子可用于模拟量子计算，这将产生重大影响。 **