Baryon Number Violation in TeV range and Asymptotic Behavior of Perturbative series

TeV范围内的重子数违规和微扰级数的渐近行为

基本信息

批准号：
05640341
负责人：
AOYAMA Hideki
金额：
$ 0.9万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

In this research, we have studied tunneling phenomena in field theories, motivated by baryon number violation processes in the standard model.One important issue is that of the inter-relation between the perturbative calculation and non-perturbative one. In models with tunneling phenomena, it is known that the perturbation theory is not summable, not even by Borel's method. Thus some cutoff for the higher order terms are necessary. We have analyzed this issue and found that when a cutoff is introduced for the above purpose, it also cuts off the perturbative-like configurations in the non-perturbative calculation, i.e., instanton-anti-instanton pair with short separation.Another interesting development is that of the Valley method. It was originally proposed to handle instanton-anti-instanton pair by myself and Kikuchi. In this research, we applied it to continuous theory for the first time and solved it for a scalar theory in 4-dim. When there is a false vacuum, a vacuum of true vacuum … More can be created by quantum tunneling. This is studied by Coleman and is known to lead to a decay rate of the false vacuum. The valley method enables one to extend Coleman's analysis for 'induced decay' of the false vacuum. We have solved the valley equation for this case and identified bubbles that are created for induced decay.We further studied the complex-time methods. It is based on the saddle-point method for Fourier transform of the time variable in the Feynman kernel. Existence of the saddle-points in the complex-time-plane leads one to deform the integration contour to complex time. In the past, it was assumed that the integration contour deformed as such go though all the physical saddle points. We have carefully analyzed this problem and managed to prove the validity of this method and identified the weights of each saddle points which were so far in the clouds.Through these research I believe that I have been able to advance our undeerstanding of various aspects of quantum tunneling phenomena. Less

在这项研究中，我们研究了野外理论中的隧道现象，这是由标准模型中的Baryon数量违规过程所激发的。一个重要问题是扰动计算与非扰动的触发性计算之间的相互关联。在具有隧道现象的模型中，众所周知，即使是Borel的方法，也无法总结扰动理论。对于高阶条款的一些截止值是必要的。我们已经分析了这个问题，并发现当出于上述目的引入截止值时，它还切断了非扰动计算中的扰动样构型，即Instanton-Anti-Instanton对具有短分离。另一个有趣的发展是山谷方法。最初建议我自己和kikuchi处理Instanton-Anti-Instanton对。在这项研究中，我们首次将其应用于连续理论，并将其解决为4-DIM的标量理论。有一个错误的真空吸尘器，真空真空……可以通过量子隧穿创建更多。这是由科尔曼（Coleman）研究的，众所周知会导致虚假真空的衰减率。山谷方法使人们可以扩展科尔曼对假真空的“诱发衰减”的分析。我们已经解决了这种情况的山谷方程，并确定了为诱发衰变而创建的气泡。我们进一步研究了复杂的时间方法。它基于Feynman内核中时间变量的傅立叶变换的鞍点方法。在复杂的时间平面中存在鞍点的存在导致一个使整合轮廓变形为复杂时间。过去，假定集成轮廓变形时，所有物理鞍点都会变形。我们已经仔细地分析了这个问题，并设法证明了这种方法的有效性，并确定了到目前为止云中的每个鞍点的权重。通过这些研究，我相信我已经能够提高我们对量子隧道现象的各个方面的不可思议。较少的