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

在这项研究中，我们研究了标准模型中受重子数破坏过程驱动的场论中的隧道现象。一个重要的问题是微扰计算和非微扰计算之间的相互关系。在具有隧穿现象的模型中，微扰理论是不可求和的，即使用Borel方法也是如此。因此，高阶项的某些截断是必要的。我们分析了这个问题，发现当为了上述目的而引入截断时，它也切断了非微扰计算中的类微扰组态，即短间隔的瞬子-反瞬子对。另一个有趣的发展是山谷方法。它最初是由我和菊池提出处理瞬子-反瞬子对的。在本研究中，我们首次将其应用于连续理论，并将其应用于四维标量理论的求解。当有假真空时，真真空…的真空量子隧道可以创造更多的东西。科尔曼对此进行了研究，已知这会导致假真空的衰减率。山谷方法使人们能够扩展科尔曼对虚假真空的“诱导衰变”的分析。我们求解了这种情况下的山谷方程，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。它是基于对Feynman核中的时间变量进行傅里叶变换的鞍点方法。复时间平面中鞍点的存在导致积分轮廓形变为复时间。在过去，人们假设积分轮廓是这样变形的，经过所有的物理鞍点。我们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每个鞍点的权重。通过这些研究，我相信我能够推进我们对量子隧道现象的各个方面的理解。较少

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