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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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Quantum mechanics. Quantumfield theory --- 530.145 --- #WSCH:AAS2 --- Quantum theory --- Quantum field theory. --- Physics --- Quantum field theory --- 530.145 Quantum theory --- $ Weak interactions(Leptonic-) --- $ Quantum electrodynamics(Radiative Corrections) --- $ Feynman graphs --- $ Scattering matrix expansion --- $ Electroweak interactions(Standard Model) --- $ Quantum electrodynamics(Regularization) --- $ Weak interactions(Gauge Theories) --- $ Quantum electrodynamics --- $ Quantum field theory --- $ Symmetry breaking in particle physics --- $ Photon covariant theory --- $ Dirac's theory --- $ Klein Gordon equation --- Théorie quantique des champs --- Weak interactions(Leptonic-) --- Quantum electrodynamics(Radiative Corrections) --- Feynman graphs --- Scattering matrix expansion --- Electroweak interactions(Standard Model) --- Quantum electrodynamics(Regularization) --- Weak interactions(Gauge Theories) --- Quantum electrodynamics --- Symmetry breaking in particle physics --- Photon covariant theory --- Dirac's theory --- Klein Gordon equation

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"Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions."--Provided by publisher.

Particles (Nuclear physics) --- S-matrix theory. --- Lie algebras --- S-matrix theory --- Algèbres de Lie --- Particules (Physique nucléaire) --- Lie algebras. --- Scattering matrix --- Matrix mechanics --- Quantum field theory --- Scattering (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Physics

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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.

Physics. --- Algebra. --- Field theory (Physics). --- Mathematical physics. --- Quantum field theory. --- String theory. --- Quantum Field Theories, String Theory. --- Field Theory and Polynomials. --- Mathematical Applications in the Physical Sciences. --- Supersymmetry. --- S-matrix theory. --- Scattering matrix --- Relativistic quantum field theory --- Unified theories --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Matrix mechanics --- Quantum field theory --- Scattering (Physics) --- Particles (Nuclear physics) --- Symmetry (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Physical mathematics --- Mathematics --- Mathematical analysis --- Models, String --- String theory --- Nuclear reactions

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Wireless power transfer allows the transfer of energy from a transmitter to a receiver across an air gap, without any electrical connections. Technically, any device that needs power can become an application for wireless power transmission. The current list of applications is therefore very diverse, from low-power portable electronics and household devices to high-power industrial automation and electric vehicles. With the rise of IoT sensor networks and Industry 4.0, the presence of wireless energy transfer will only increase. In order to improve the current state of the art, models are being developed and tested experimentally. Such models allow simulating, quantifying, predicting, or visualizing certain aspects of the power transfer from transmitter(s) to receiver(s). Moreover, they often result in a better understanding of the fundamentals of the wireless link. This book presents a wonderful collection of peer-reviewed papers that focus on the modelling of wireless power transmission. It covers both inductive and capacitive wireless coupling and includes work on multiple transmitters and/or receivers.

History of engineering & technology --- resonance-based wireless power transfer (R-WPT) --- resonance frequency --- power transfer efficiency (PTE) --- 3-coil system --- steady-state matrix analysis --- Class-E power amplifier --- wireless power transfer (WPT) system --- output characteristics --- strength --- coupling coefficient --- impedance matrix --- multiple coils --- mutual inductance --- scattering matrix --- transfer impedance --- wireless power transfer --- design optimization --- finite element analysis --- gallium nitride --- gradient methods --- inductive power transmission --- power measurement --- transformer cores --- wireless charging --- circuit modeling --- numerical analysis --- capacitive wireless power transfer --- resonance --- power-transfer efficiency --- multiports --- multiple-input single-output --- wireless power transmission --- electric field --- shielded-capacitive power transfer --- design guidelines --- resonant --- inductive coupling --- optimal load --- single-input multiple-output --- power gain