Scattering in Quantum Field Theories: The Axiomatic and Constructive Approaches
Scattering in Quantum Field Theories: The Axiomatic and Constructive Approaches
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量子场论中的散射：公理化和构造性方法
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发表时间：
2014
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通讯作者：
D. Iagolnitzer
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作者：
D. Iagolnitzer
量子场论的公理化和构造性方法首先旨在将其建立在精确的，非微扰的基础上：分别是一般公理和特定理论的严格定义。从粒子物理学的观点来看，目标是发展一个相对论散射理论，包括粒子分析和推导碰撞振幅的一般性质。考虑到连续的改进，这本书提供了一个现代的，独立的，和连贯的介绍在过去20年的重要发展，其中大部分没有处理或详细讨论在以前的书籍。这些发展特别包括公理推导，在大量的理论，一般因果和动量空间解析性质的多粒子碰撞振幅;建设性的定义，最初在（非物理的）欧几里得空间，各种模型，包括非超重整化理论在20世纪80年代通过相空间扩展处理;以及随后的散射理论的建设性方法，它提供了在越来越高的能量区域的质谱，渐近完整性和多粒子结构的信息。
Axiomatic and constructive approaches to quantum field theory first aim to establish it on precise, non-perturbative bases: general axioms and rigorous definitions of specific theories respectively. From the viewpoint of particle physics, the goal is then to develop a relativistic scattering theory, including particle analysis and the derivation of general properties of collision amplitudes. Taking into account successive improvements, this book provides a modern, self-contained, and coherent presentation of important developments over the last 20 years, most of which have not been treated or discussed in detail in earlier books. These developments include in particular the axiomatic derivation, in massive theories, of general causal and momentum-space analyticity properties of multiparticle collision amplitudes; the constructive definition, initially in the (unphysical) Euclidean space, of various models including non-super-renormalizable theories treated in the 1980s via phase-space expansions; and the subsequent constructive approach to scattering theory, which provides information on the mass spectrum, asymptotic completeness, and multiparticle structure in increasingly higher energy regions.