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

本文研究了场论中由标准模型中重子数破坏过程引起的隧穿现象，其中一个重要问题是微扰计算与非微扰计算之间的相互关系。在隧道现象的模型中，已知微扰理论是不可求和的，即使用波莱尔方法也不行。因此，高阶项的某些截止是必要的。我们对这个问题进行了分析，发现当为了上述目的引入截断时，它也截断了非微扰计算中的类微扰构型，即，另一个有趣的发展是Valley方法。我和菊池最初提出处理瞬子-反瞬子对。在本研究中，我们首次将其应用于连续理论，并求解了四维标量理论。 ...更多信息 可以通过量子隧穿产生。这是由科尔曼研究，并已知导致假真空的衰减率。谷方法使人们能够扩展科尔曼对假真空的“诱导衰变”的分析。我们已经解决了这种情况下的谷方程，并确定了诱导衰变产生的气泡。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方法。在复时间平面上的鞍点的存在导致一个变形的积分轮廓复时间。在过去，假设这样变形的积分轮廓通过所有的物理鞍点。我们对这个问题进行了仔细的分析，并证明了这种方法的有效性，确定了目前为止在云中的每个鞍点的权重，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

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