Topics in Model Theory

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【簡介】 This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods. The second is an introduction to "continuous logic" or "continuous model theory," drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic. These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021. 【目錄】 Sample Chapter(s) Preface Chapter 1: Stability Theory Contents: Preface Stability Theory: Introduction Preliminaries Stability Continuous Logic: Introduction Background "Official" Continuous Logic Stability in Continuous Logic Index Readership: Graduate students and researchers in mathematics and related subjects interested in model theory and its applications.

Advanced Topics in Quantum Mechanics (1版)

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Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout. Covers many advanced mathematical techniques in quantum mechanics, each illustrated with detailed examples Presents two alternative formulations of quantum mechanics; the path integral and phase space formulations, which are useful in advanced applications Provides a pedagogical and thorough overview of the exact WKB method, which plays an increasingly important role in many areas of modern physics