In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from the perturbative expansion about the perturbative vacuum, combined with a single global boundary condition. This provides a dramatic realization of the principle of "resurgence", that the fluctuations about different semiclassical saddle points are related to one another in a precise quantitative manner. The analysis of quantum mechanics also generalizes to certain calculable regimes of quantum field theory.
In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative results can be encoded in a suitable modified perturbative series in a class of quantum mechanical problems. We illustrate this explicitly in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.
Linear perturbations of an exact gravitational wave in the Bianchi IV universe
Tomsk State Pedagogical University（托木斯克国立师范大学）；Tomsk State University of Control Systems and Radioelectronics（托木斯克国立控制与无线电电子大学）；National Research Tomsk State University（托木斯克国立研究大学）
The main objective of this thesis is to present a new analytical framework for low-energy QCD that goes under the name of massive, or "screened", perturbative expansion. The massive perturbative expansion is motivated by the phenomenon of dynamical mass generation, by which the gluons acquire a mass of the order of the QCD scale $Λ_{\text{QCD}}$ in the limit of vanishing momentum. It is a simple extension of ordinary perturbation theory that consists in a shift of the expansion point of the Yang-Mills perturbative series with the aim of treating the transverse gluons as massive already at tree…
From BTZ Perturbations to Schwarzian Modes: A Geometrical and Perturbative Analysis
Instituto de Física La Plata (IFLP), CONICET & Departmento de Física Dr. Emil H. Bose, UNLP（拉普拉塔物理研究所（IFLP），CONICET & 恩里克·H·博斯物理学系，拉普拉塔国立大学）；Instituto de Astronomía y Física del Espacio, (CONICET-UBA)（天体与空间物理研究所（CONICET-UBA））
Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions
我们分析了de Sitter和anti de Sitter空间中大质量标量的有效拉格朗日密度的微扰弱场展开的高阶行为，并表明这种微扰信息不足以描述这些理论的非微扰行为，与恒定电场和磁场背景场中带电标量的Euler-Heisenberg有效拉格朗日密度的类似情况相反.例如，在偶数维的德西特空间中有粒子产生，但有效拉格朗日密度仍然是实数，即使它的弱场展开是一个发散的非交错级数，其形式虚部对应于正确的粒子产生率。这个明显的难题可以通过考虑相关费曼传播子的完整非微扰结构来解决，而不能仅仅从微扰展开来解决。
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Appl…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory. After that we prove that gauge invariance restricts severely the possible finite renormalizations, so at least in the second order of the perturbation theory, the model is renormalizable.
We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renomalization of this model defined in R^3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalized traces of ISU(2) holonomies associated with oriented, framed and coloured …
The quark gluon plasma is formed in heavy-ion collisions, and it can be described by solutions of relativistic hydrodynamics. In this paper we utilize perturbative hydrodynamics, where we study first order perturbations on top of a known solution. We investigate the perturbations on top of the Hubble flow. From this perturbative solution we can give the form of the particle emitting source and calculate observables of heavy-ion collisions. We describe the source function and the single-particle momentum spectra for a spherically symmetric solution.
Università degli Studi di Ferrara（费拉拉大学）；INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；Università di Padova（帕多瓦大学）；INFN Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF-Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
In this work, we present the quasinormal modes of a fermionic field in the background of Gauss-Bonnet-AdS black holes. We find exact solutions for $D=5$ at the fixed value $α=R^2/2$ of the Gauss--Bonnet coupling constant, with $R$ denoting the AdS radius, and we find numerical solutions for some range of values of the coupling constant $α$ and $D=5, 6$. Mainly, we find two branches of quasinormal frequencies, a branch perturbative in the Gauss-Bonnet coupling constant $α$, and another branch nonperturbative in $α$. The phenomena of nonperturbative modes, which seem to be quite general in theor…
We investigate the relation between the time-ordered vacuum correlation functions for interacting real scalar fields in Minkowski spacetime and in the Rindler wedge. The correlation functions are constructed perturbatively within the in-in formalism, often employed in calculations in more general spacetimes. We prove to all orders in perturbation theory that the time-ordered vacuum correlation functions can be calculated in the in-in formalism with internal vertices restricted to any Rindler wedge containing the external points. This implies that the Minkowski in-in (or in-out) perturbative ex…
