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This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.

S-matrix theory. --- Scattering matrix --- Matrix mechanics --- Quantum field theory --- Scattering (Physics)

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Extensively classroom-tested, A Course in Field Theory provides material for an introductory course for advanced undergraduateand graduate students in physics. Based on the author’s course that he has been teaching for more than 20 years, the text presents complete and detailed coverage of the core ideas and theories in quantum field theory. It is ideal for particle physics courses as well as a supplementary text for courses on the Standard Model and applied quantum physics.

Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Cross Sections --- Path Integrals For Fermions --- Quantisation Of Fields --- The Higgs Mechanism --- The Scattering Matrix

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Based on the popular Artech House title Microwave Network Design Using the Scattering Matrix, this authoritative resource provides comprehensive coverage of the wave approach to microwave network characterization, analysis, and design using scattering parameters. New topics include signal and noise analysis of differential microwave networks based on mixed mode wave variables, generalized mixed mode scattering, and generalized mixed mode noise wave scattering matrix.nThis one of a kind resource presents all aspects and topics related to the scattering matrix which have been developed and applied in microwave theory and practice. The book is an excellent source of theoretical information on the wave variables and scattering matrix and their application to microwave network characterization, modeling, analysis and design. This book demonstrates the approach of noise and signal analysis and how it is applicable to two port networks and their cascades, multi-ports and multi-element multiport networks with standard single-ended ports with differential ports and simultaneously with single-ended and differential ports. It is suitable for beginners, and students as well as experienced engineers and researchers working in the field of microwaves.

Microwave circuits. --- Microwave communication systems. --- S-matrix theory. --- Circuits, Microwave --- Electronic circuits --- Microwave devices --- Scattering matrix --- Matrix mechanics --- Quantum field theory --- Scattering (Physics) --- Intercommunication systems --- Telecommunication systems --- Line-of-sight radio links

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Quantum mechanics. Quantumfield theory --- S-matrix theory --- 530.145 --- 517.984.4 --- Scattering matrix --- Matrix mechanics --- Quantum field theory --- Scattering (Physics) --- Quantum theory --- Spectral theory in Hilbert spaces --- S-matrix theory. --- 517.984.4 Spectral theory in Hilbert spaces --- 530.145 Quantum theory

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Quantum field theory --- Congresses --- -Regge theory --- -S-matrix theory --- -530.1 --- Scattering matrix --- Matrix mechanics --- Scattering (Physics) --- Angular momentum (Nuclear physics) --- Particles (Nuclear physics) --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Amateurs' manuals --- -Amateurs' manuals --- Basic principles of physics --- 530.1 Basic principles of physics --- Regge theory --- S-matrix theory --- 530.1 --- Congresses&delete& --- Quantum field theory - Congresses