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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 Feynmanintegrals 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.

This book presents the better understanding of infrared structures of particle scattering processes in quantum electrodynamics (QED) in four-dimensional spacetime. An S-matrix is the fundamental quantity in scattering theory. However, if a theory involves massless particles, such as QED and gravity, the conventional S-matrix has not been well defined due to the infrared divergence, and infrared dynamics thus needs to be understood in-depth to figure out the S-matrix. The book begins with introducing fundamental nature of the charge conservation law associated with asymptotic symmetry, and explaining its relations to soft theorems and memory effect. Subsequently it looks into an appropriate asymptotic state of the S-matrix without infrared divergences. The Faddeev-Kulish dressed state is known as a candidate of such a state, and its gauge invariant condition and its relation to the asymptotic symmetry are discussed. It offers an important building blocks for constructing the S-matrix without infrared divergences.

Radar polarimetry has been highly sought after for its use in the precise monitoring of Earth's surface. Polarimetric SAR Imaging explains the basic concepts of polarimetry and its diverse applications including: deforestation, tree classification, landslide detection, tsunamis, volcano eruptions and ash distribution, snow accumulation, rice field monitoring, urban area exploration, ship detection, among other applications. The explanations use actual data sets taken by Advanced Land Observing Satellite (ALOS and ALOS2). With the increasing problems presented by climate change, there is a growing need for detailed earth observation using polarimetric data. As the treatment of vector nature of radar waves is complex, there is a gap between the theory and the application. Polarimetric SAR Imaging: Theory and Applications addresses and fills this gap. Features: Provides cutting-edge polarimetric applications for earth observation with full color images. Includes detailed descriptions of theory, equations, expansions, and flowcharts, and numerous real examples. Explains concepts, data analysis, and applications in simple and clear language aimed at an intuitive comprehension. Provides specific and unique examples of PolSAR images derived from actual space and airborne systems (ALOS/ALOS2, PiSAR-x/L) Covers the wide range of the radar polarimetry, especially the decomposition of the polarimetry data, an original method developed by the author using the Japanese polarimetric SAR data Illustrated in full color using images generated by polarimetric techniques, this book is easy to understand and use for both student and expert, and is an excellent resource both in the classroom and in the field.

Using the analyticity property of the amplitudes of physical processes allows one to obtain important relations connecting various physical quantities. These relations can be established without specifying the concrete form of the interaction between particles, which is often poorly known. The analytic methods make use of the unitarity property of the S-matrix and the formalism of the Feynman diagrams. The present book is devoted to a systematic description of the analytic and diagram methods in the theory of nuclear reactions at low and intermediate energies. First, a general overview of the unitarity and analyticity properties of the S- and T-matrices is presented. Then the general theory of non-relativistic Feynman diagrams, their specific features and the analytic properties of their amplitudes is described. Three- and four-prong vertex functions of the non-relativistic Feynman diagrams are among the topics that are addressed and discussed, including the important relation between vertex functions and the asymptotic form of the nuclear bound-state wave functions. Specific approaches to describing nuclear reactions, which use analytic and diagram methods are outlined. These methods include the dispersion K-matrix approach, the dispersion relations, and the Trojan horse method. A part of the book deals with the asymptotic normalization coefficients (ANCs). ANCs are fundamental nuclear characteristics that are important in nuclear reaction and nuclear structure physics as well as in nuclear astrophysics. They are used actively in the analysis of nuclear reactions, in particular in considering the creation of elements in the Universe. Various methods of determining ANCs are overviewed. One chapter of the book is devoted to the methods of obtaining information on the features of bound nuclear states by an analytic continuation of the scattering data. The analytic continuation of the Lippmann-Schwinger and Faddeev integral equations onto unphysical energy sheets, which can be used for finding the position and width of resonances and the virtual (antibound) states is described. A generalization of wave function normalization to the Gamow states is outlined.

The author introduces the supersymmetric localization technique, a new approach for computing path integrals in quantum field theory on curved space (time) defined with interacting Lagrangian. The author focuses on a particular quantity called the superconformal index (SCI), which is defined by considering the theories on the product space of two spheres and circles, in order to clarify the validity of so-called three-dimensional mirror symmetry, one of the famous duality proposals. In addition to a review of known results, the author presents a new definition of SCI by considering theories on the product space of real-projective space and circles. In this book, he explains the concept of SCI from the point of view of quantum mechanics and gives localization computations by reducing field theoretical computations to many-body quantum mechanics. He applies his new results of SCI with real-projective space to test three-dimensional mirror symmetry, one of the dualities of quantum field theory. Real-projective space is known to be an unorientable surface like the Mobius strip, and there are many exotic effects resulting from Z2 holonomy of the surface. Thanks to these exotic structures, his results provide completely new evidence of three-dimensional mirror symmetry. The equivalence expected from three-dimensional mirror symmetry is transformed into a conjectural non-trivial mathematical identity through the new SCI, and he performs the proof of the identity using a q-binomial formula.

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. This 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.

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.

The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source — injecting electrons with time delay much larger than the electron coherence time — is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.

This authoritative resource provides you with comprehensive and detailed coverage of the wave approach to microwave network characterization, analysis, and design using scattering parameters. For the first time in any book, all aspects and approaches to wave variables and the scattering matrix are explored. The book compares and contrasts voltage waves, travelling waves, pseudo waves, and power waves, and explains the differences between real scattering parameters, pseudo scattering parameters, and power scattering parameters. You find important discussions on standard scattering matrices and wave quantities, mixed mode wave variables, and noise wave variables with noise wave correlation matrices. Moreover, the book presents clear methods for standard single ended multiport network design and noise analysis. This in-depth reference is packed with over 1,100 equations and numerous illustrations.