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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

在本研究中，我们研究了由标准模型中的重子数违反过程激发的场理论中的隧道现象。一个重要的问题是微扰计算与非微扰计算之间的相互关系。在有隧道现象的模型中，我们知道微扰理论是不可和的，即使用Borel方法也是不可和的。因此，需要对高阶项进行截断。我们对这一问题进行了分析，发现为上述目的引入截断时，也截断了非微扰计算中的类微扰构型，即短分离的瞬子-反瞬子对。另一个有趣的发展是山谷方法。本来是我和菊地提出处理瞬子-反瞬子对的。在本研究中，我们首次将其应用于连续理论，并对4-dim的标量理论进行了求解。当有一个假真空，一个真正真空的真空…更多的可以通过量子隧穿产生。这是科尔曼研究过的，已知会导致假真空的衰减率。谷值法使人们能够扩展Coleman对假真空的“诱导衰减”的分析。我们已经解决了这种情况下的山谷方程，并确定了为诱导衰变而产生的气泡。我们进一步研究了复时间方法。它是基于费曼核中时间变量的傅里叶变换的鞍点法。复时间平面上鞍点的存在导致积分轮廓变形为复时间。过去，我们假设积分轮廓的变形是这样经过所有物理鞍点的。我们仔细地分析了这个问题，并设法证明了该方法的有效性，并确定了到目前为止在云中每个鞍点的权重。通过这些研究，我相信我已经能够推进我们对量子隧穿现象的各个方面的理解。少