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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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"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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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.

Physics. --- Quantum field theory. --- String theory. --- Gravitation. --- Cosmology. --- Quantum Field Theories, String Theory. --- Classical and Quantum Gravitation, Relativity Theory. --- Quantum gravity. --- Quantum chromodynamics. --- S-matrix theory. --- Scattering matrix --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Gravity, Quantum --- Particles (Nuclear physics) --- Quantum electrodynamics --- General relativity (Physics) --- Gravitation --- Quantum theory --- Matrix mechanics --- Quantum field theory --- Scattering (Physics) --- Astronomy --- Deism --- Metaphysics --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Properties

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This book is a comprehensive set of articles reflecting the latest advances and developments in mathematical modeling and the design of electrical machines for different applications. The main models discussed are based on the: i) Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series in 2-D or 3-D with a quasi-Cartesian or polar coordinate system); ii) electrical, thermal and magnetic equivalent circuit; iii) hybrid model. In these different papers, the numerical method and the experimental tests have been used as comparisons or validations.

surface-mounted PM machines --- torque pulsation --- magnet shape optimization --- analytical expression --- 2D --- electromagnetic performances --- finite iron relative permeability --- numerical --- sinusoidal current excitation --- subdomain technique --- switched reluctance machine --- scattering matrix --- Fourier analysis --- permanent magnet machines --- analytical modeling --- analytical model --- high-speed --- sleeve --- non-homogeneous permeability --- permanent-magnet --- partial differential equations --- separation of variable technique --- electrical machines --- surface inset permanent magnet --- electric machines --- permanent magnet motor --- rotating machines --- hybrid excitation --- magnetic equivalent circuits --- 3D finite element method --- eddy-current losses --- experiment --- hybrid model --- magnetic equivalent circuit --- Maxwell–Fourier method --- analytical method --- eddy-current --- finite-element analysis --- loss reduction --- permanent-magnet losses --- thermal analysis --- linear induction motors --- complex harmonic modeling --- hybrid analytical modeling --- 2D steady-state models --- multiphase induction machine --- reduced order --- rotor cage --- torque pulsations --- multi-phase --- segmentation --- synchronous machines --- thermal equivalence circuit --- Voronoï tessellation --- winding heads --- nodal method --- thermal resistances --- n/a --- Maxwell-Fourier method --- Voronoï tessellation