Find What the Best MBAs Know by Peter Navarro in Hardcover and other formats in Business & Economics > Leadership.

Find What Is the Story of Batman? by Michael Burgan in Paperback and other formats in Juvenile Nonfiction > Comics & Graphic Novels - Biography.

Find The Secrets to Writing a Successful Business Plan by Hal Shelton in Paperback and other formats in Business & Economics > Entrepreneurship.

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.

"Since its establishment in 1965, Business Economics has been an essential resource for those who use economics in the workplace. Its consistent intent has been to distinguish itself from academic journals by focusing on what is useful to practitioners of economics in their everyday work, and it has risen to become the leading forum for debating solutions to critical business problems, analyzing key business and economic issues, and sharing of best-practice models, tools, and hands-on techniques. In celebration of the journal's anniversary, The Best of ""Business Economics"" brings together forty of the best articles from half a century of publication: those that pushed boundaries, challenged conventional wisdom, and redefined the way practitioners and academics approached their work. Much of the insight afforded in this collection on the uses and limitations of economics are as fresh and useful today as when they were published. Featuring award-winning articles and the world's premier economists, this collection is an essential addition to any economics library."

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Many people have a question, China's mobile payment is very developed, why does the United States still like to use credit cards so much? What is the reason for this difference? If I go to the United States, how do I use credit cards?

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