Surveys of Modern Mathematics, Volume 15
TEXTBOOK
To Be Published: 15 March 2020
Publisher: International Press of Boston, Inc.
Paperback
188 pages}
This new textbook is based upon the notes that accompany the authorfs graduate course gAlgebraic Geometry Ih at Tsinghua University.
Much of commutative algebra owes its existence to algebraic geometry and vice versa, and this is why there is no clear border between the two. In learning algebraic geometry, you not only learn more commutative algebra, but also develop a geometrical way of thinking about it.
Eduard J. N. Looijenga is one of the best algebraic geometers in the world and a leading mathematician of his generation. He is a member of the Royal Netherlands Academy of Arts and Sciences and currently teaches at Tsinghua University.
This volume is part of the Surveys of Modern Mathematics book series.
Hardback
Published: 10 January 2020
320 Pages | 39 illustrations
246x171mm
ISBN: 9780198827856
Paperback
ISBN: 9780198827863
Novel presentation of equations as recipes aids comprehension
Demystifies the most iconic equations of quantum mechanics
Clear presentation, suitable for all courses covering quantum mechanics
Provides philosophical context typically absent in other textbooks
Quantum mechanics is an extraordinarily successful scientific theory. But it is also completely mad. Although the theory quite obviously works, it leaves us chasing ghosts and phantoms; particles that are waves and waves that are particles; cats that are at once both alive and dead; lots of seemingly spooky goings-on; and a desperate desire to lie down quietly in a darkened room. The Quantum Cookbook explains why this is. It provides a unique bridge between popular exposition and formal textbook presentation, written for curious readers with some background in physics and sufficient mathematical capability. It aims not to teach readers how to do quantum mechanics but rather helps them to understand how to think about quantum mechanics. Each derivation is presented as a 'recipe' with listed ingredients, including standard results from the mathematician's toolkit, set out in a series of easy-to-follow steps. The recipes have been written sympathetically, for readers who - like the author - will often struggle to follow the logic of a derivation which misses out steps that are 'obvious', or which use techniques that readers are assumed to know.
1: Planck's Derivation of E = hn: The Quantisation of Energy
2: Einstein's Derivation of E = mc2: The Equivalence of Mass and Energy
3: Bohr's Derivation of the Rydberg Formula: Quantum Numbers and Quantum Jumps
4: De Broglie's Derivation of / = h/p: Wave-particle Duality
5: Schrodinger's Derivation of the Wave Equation: Quantisation as an Eigenvalue Problem
6: Born's Interpretation of the Wavefunction: Quantum Probability
7: Heisenberg, Bohr, Robertson, and the Uncertainty Principle : The Interpretation of Quantum Uncertainty
8: Heisenberg's Derivation of the Pauli Exclusion Principle: The Stability of Matter and the Periodic Table
9: Dirac's Derivation of the Relativistic Wave Equation: Electron Spin and Antimatter
10: Dirac, Von Neumann, and the Derivation of the Quantum Formalism: State Vectors in Hilbert Space
11: Von Neumann and the Problem of Quantum Measurement: The 'Collapse of the Wavefunction'
12: Einstein, Bohm, Bell, and the Derivation of Bell's Inequality: Entanglement and Quantum Non-locality
Oxford Graduate Texts
Comprehensive updated synthesis of statistical physics and quantum field theory
Introduction to new and powerful methods of analysis
Ideal combination of physical ideas and mathematical tools
Mathematical background provided in supplements at end of each chapter
Four new chapters on Boundary Field Theory, Semiclassical Methods in Bosonic Field Theories, Semiclassical Methods in Fermionic Field Theories, and Truncated Hilbert Space Approach
Several new sections, including Entanglement Entropy and the LeClair-Mussardo formula
New references
New exercises
Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions.
Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.
Lecture Notes of the Les Houches Summer School: Volume 108, July 2017
Comprehensive introduction to in-use Effective Field Theories
Detailed and pedagogical insight into Effective Field Theory for students and practitioners
Includes latest developments and current trends by leading scholars in the field
The topic of the CVIII session of the Ecole de Physique des Houches, held in July 2017, was Effective Field Theory in Particle Physics and Cosmology. Effective Field Theory (EFT) is a general method for describing quantum systems with multiple length scales in a tractable fashion. It allows to perform precise calculations in established models (such as the Standard Models of particle physics and cosmology), as well as to concisely parametrise possible effects from physics beyond the Standard Models.
The goal of this school was to offer a broad introduction to the foundations and modern applications of Effective Field Theory in many of its incarnations. This is all the more important as there are preciously few textbooks covering the subject, none of them in a complete way. In this book, the lecturers present the concepts in a pedagogical way so that readers can adapt some of the latest developments to their own problems. The chapters cover almost all the lectures given at the school and will serve as an introduction to the topic and as a reference manual to students and researchers.
1: Renormalization Theory and Effective Field Theories, Matthias Neubert
2: Introduction to Effective Field Theories, Aneesh V. Manohar
3: Effective Field Theory with Nambu?Goldstone Modes, Antonio Pich
4: Introduction to Effective Field Theories and Inflation, C.P. Burgess
5: Lectures on Soft-Collinear Effective Theory, Thomas Becher
6: Effective Field Theories forNuclear and (some) Atomic Physics, U. van Kolck
7: Effective Field Theory of Large Scale Structure, T. Baldauf
8: Effective Theories for Quark Flavour Physics, Luca Silvestrini
9: Effective Field Theories for Heavy Quarks: Heavy Quark Effective Theory and Heavy Quark Expansion, Thomas Mannel
10: Heavy Quark Effective Theory: a predictive EFT on the lattice, Rainer Sommer
11: Effective theory approach to direct detection of dark matter, Junji Hisano
12: Solutions to Problems at Les Houches Summer School on EFT