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

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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