International Series of Monographs on Physics
Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics.
As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale.
Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized.
This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.
Preface
1:Gaussian integrals. Algebraic preliminaries
2:Euclidean path integrals and quantum mechanics
3:Quantum mechanics: Path integrals in phase space
4:Quantum statistical physics: Functional integration formalism
5:Quantum evolution: From particles to fields
6:The neutral relativistic scalar field
7:Perturbative quantum field theory: Algebraic methods
8:Ultraviolet divergences: Effective quantum field theory
9:Introduction to renormalization theory and renormalization group
10:Dimensional continuation, regularization. Minimal subtraction, RG functions
11:Renormalization of local polynomials. Short distance expansion
12:Relativistic fermions: Introduction
13:Symmetries, chiral symmetry breaking and renormalization
14:Critical phenomena: General considerations. Mean-field theory
15:The renormalization group approach: The critical theory near dimension 4
16:Critical domain: Universality, "-expansion
17:Critical phenomena: Corrections to scaling behaviour
18:O(N)-symmetric vector models for N large
19:The non-linear ?-model near two dimensions: Phase structure
20:Gross-Neveu-Yukawa and Gross-Neveu models
21:Abelian gauge theories: The framework of quantum electrodynamics
22:Non-Abelian gauge theories: Introduction
23:The Standard Model of fundamental interactions
24:Large momentum behaviour in quantum field theory
25:Lattice gauge theories: Introduction
26:BRST symmetry, gauge theories: Zinn-Justin equation and renormalization
27:Supersymmetric quantum field theory: Introduction
28:Elements of classical and quantum gravity
29:Generalized non-linear ?-models in two dimensions
30:A few two-dimensional solvable quantum field theories
31:O(2) spin model and Kosterlitz-Thouless's phase transition
32:Finite-size effects in field theory. Scaling behaviour
33:Quantum field theory at finite temperature: Equilibrium properties
34:Stochastic differential equations: Langevin, Fokker-Planck equations
35:Langevin field equations, properties and renormalization
36:Critical dynamics and renormalization group
37:Instantons in quantum mechanics
38:Metastable vacua in quantum field theory
39:Degenerate classical minima and instantons
40:Perturbative expansion at large orders
41:Critical exponents and equation of state from series summation
42:Multi-instantons in quantum mechanics
Bibliography
Index
Oxford Graduate Texts
Quasi-adiabatic theory has broad applications across disciplines, from quantum computing and cosmology to materials science and atomic physics. This textbook offers a comprehensive introduction to quasi-adiabatic effects and their applications.
In modern physics, the term "adiabatic" refers to the infinitely slow evolution limit. Quasi-adiabatic theory, by contrast, describes time-dependent processes that are slow but not truly adiabatic. This theory is especially rich in effects that can be understood even in systems with complex many-body interactions. Examples from research in quantum computing, phase transitions, ultra-cold atoms, and quantum control are used throughout the book.
Quasi-Adiabatic Effects: Introduction to Geometric Phases and Landau-Zener Transitions is aimed at undergraduate and graduate students, interested in more advanced quantum and classical mechanics, as well as researchers who deal with nonequilibrium physics. The book is also an excellent illustration of methods of complex analysis applied in these fields. Several topics, such as the Dykhne formula (Chapter 7) and multistate Landau-Zener theory (Chapter 11), are discussed here for the first time in a textbook style.
In addition, readers will find numerous thoughtfully designed problems, complete with solutions.
1:Introduction
2:Time-dependent Schrodinger equation
3:Geometric phase
4:Geometric phase effects in electric currents
5:Landau-Zener-Majorana-Stuckelberg formula
6:Beyond the Landau-Zener formula
7:Dykhne formula
8:Nonadiabatic transitions and decoherence
9:Nonadiabatic critical phenomena
10:Quasi-adiabatic dynamics in classical mechanics
11:Multistate Landau-Zener problem
Appendix A: Euler's Gamma function
Index
Oxford Mathematical Monographs
The Mittag-Leffler function is a basic function in fractional calculus and is an entire function in the complex plane. Entire functions are generalization of polynomials to infinite degree, do not have singularities in the complex plane, and possess a wealth of beautiful properties. Entire functions are defined by a Taylor series that converges for any finite complex number. In addition to the summation formulation and as a consequence of Weierstrass's factorization theorem, entire functions possess a product form in which all zeros appear.
The study of properties of entire functions has led Mittag-Leffler, around 1900, to the study of his function. The Mittag-Leffler function is a primary example of an entire function, tunable in its order, and is represented by the simple eyeing Taylor series, in which another basic complex function, the Gamma function pops up.
The Mittag-Leffler and Gamma Function mainly targets the mathematical properties of the Mittag-Leffler function in easy-to-understand language, not its applications to fractional analysis nor its numerical evaluation. Since the Gamma function plays a crucial role in the properties of the Mittag-Leffler function, a comprehensive treatment of the Mittag-Leffler function requires the knowledge of the Gamma function. The second part of the book attempts to present a complete study, enriched with historical references.
Hardback
Published: 06 May 2026 (Estimated)
224 Pages
234x156mm
ISBN: 9780198993377
Format: Paperback / softback, 246 pages, height x width: 235x155 mm, 90 Illustrations, black and white
Series: Compact Textbooks in Mathematics
Pub. Date: 19-Apr-2026
ISBN-13: 9783032198617
This textbook provides a comprehensive and rigorous treatment of the mathematical theory underlying rigidity and the flexibility of frameworks. Integrating classical geometry, modern rigidity theory, and topological methods, the authors develop a unified perspective on how geometric constraints determine the possible motions and configurations of planar and spatial structures.
The book begins by discussing the foundations of rigid motions, infinitesimal rotations, and vector fields, establishing the analytical and algebraic tools required for later chapters. The book then advances to a systematic study of unit-bar frameworks, infinitesimal rigidity, the rigidity matrix, rigidity of graphs and the rigidity and flexibility of a polyhedral surface. Each chapter is accompanied by exercises, with complete solutions provided in the final chapter.
Throughout the book, the authors incorporate historical context, classical theorems, and modern applications in robotics and computational geometry. This book is suitable as a graduatelevel textbook for a course on the geometry of frameworks or as a reference for researchers in geometry, combinatorics, and related applied fields.
Chapter 1. Motions and velocity vector felds.
Chapter 2. Motions of frameworks.
Chapter 3. Unit-bar frameworks.
Chapter 4. Infinitesimal motions.
Chapter 5. Rigidity of graphs in the plane.
Chapter 6. Rigidity of graphs in R^d.
Chapter 7. Flexible polyhedral surfaces in R^3.
Chapter 8. Addendum.
Chapter 9. Solutions to the exercises.
Format: Paperback / softback, 505 pages, height x width: 235x155 mm, XVII, 505 p.
Series: Universitext
Pub. Date: 24-Apr-2026
ISBN-13: 9781071652374
The aim of this text is to present fundamental ideas, results, and techniques concisely, mainly in matrix theory with some in linear algebra. The book contains ten chapters covering various topics ranging from rank, similarity, and special matrices, to Schur complements, matrix normality, and majorization. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this third edition include:
expansion of topics such as eigenvalue continuity, matrix functions, nonnegative matrices, matrix norms, and majorization inclusion of more than 200 examples and more than 1500 exercises emphasis on basic techniques and skills for partitioned matrices through which a variety of matrix results and matrix inequalities are shown showcase of many majorization-type inequalities for diagonal entries, eigenvalues, and singular values of matrices.
This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for advanced undergraduate or graduate students. Prerequisites include a solid background in elementary linear algebra and calculus. The text can also serve as a reference for researchers in algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other scientific areas.
Preface to the Third Edition.- Frequently Used Notation and
Terminology.- Frequently Used Terms.-
1. Elementary Linear Algebra Review.-
2. Partitioned Matrices, Rank, and Eigenvalues.-
3. Matrix Polynomials and Canonical Forms.-
4. Numerical Ranges, Norms, and Special Products of Matrices.-
5. Special Types of Matrices.-
6. Unitary Matrices and Contractions.-
7. Positive Semidefinite Matrices.-
8. Hermitian Matrices.-
9. Normal Matrices.-
10. Majorization and Matrix Inequalities.-
References.-
Notation.-
Index.
Format: Hardback, 159 pages, height x width: 235x155 mm, 5 Illustrations, color; 6 Illustrations, black and white
Series: Trends in Mathematics
Pub. Date: 11-May-2026
ISBN-13: 9783032200976
This volume is based on the talks presented at the "New Frontiers in Homogenization and Fractional Calculus" conference, held at CRM-Barcelona on March 2425, 2025. This event was organized to celebrate the 50th anniversary of the mathematical technique of Gamma-convergence, introduced by Ennio De Giorgi and Tullio Franzoni in 1975. Originally developed for applied purposes, this technique remains a fundamental tool in the study of various scientific phenomena, such as homogenization, phase transitions, and the asymptotic analysis of partial differential equations. At the same time, there has been a growing interest in the study of nonlocal problems, particularly due to their relevance in probability theory. In addition to representing a particularly challenging area of mathematics, these problems have become increasingly relevant in material science applications.
The contributions in this volume cover a wide range of topics and reflect the main areas of current research in variational convergence and nonlocal analysis. Additionally, as these techniques extend beyond pure analytical theory, the contributions explore numerical applications. This volume is aimed at students and researchers in mathematics, physics, and engineering who are interested in exploring recent developments in the theories of homogenization and fractional calculus.
Chapter 1. Singular-perturbation problems in fractional Sobolev spaces recent results.
Chapter 2. A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces.
Chapter 3. The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities.
Chapter 4. Numerical Approximation of the logarithmic Laplacian via sinc-basis.
Chapter 5. A survey on the resolvent convergence.-
Chapter 6. Fractional Sobolev spaces via interpolation, and applications to mixed local-nonlocal operators.
Chapter 7. Some results about strongly degenerate parabolic equations and forward-backward parabolic equations.-
Chapter 8. A survey on anisotropic integral representation results.
Format: Hardback, 468 pages, height x width: 235x155 mm, XVI, 468 p.
Series: Mathematics for Sustainable Developments
Pub. Date: 13-May-2026
ISBN-13: 9789819571338
This book offers a comprehensive collection of 35 research contributions that explore the diverse and growing impact of machine learning across various domains. By aligning its themes with Sustainable Development Goals (SDG9: Industry, Innovation and Infrastructure), the book examines the practical applications ranging from healthcare, agriculture, cybersecurity and renewable energy systems to natural language processing, education and defense technologies. Each contribution highlights contemporary challenges, innovative methodologies and real-world implementations, offering insights into the interdisciplinary nature of machine learning research. The book serves as a valuable reference for researchers, practitioners and students interested in the evolving applications of machine learning to address complex and multidisciplinary problems.
A Comprehensive Review of Vison Language Models in the Realm of Full
Self Driving Systems.- Optimal Defense Strategies for Security Agencies: A
Dual Hesitant Fuzzy Matrix Game Approach.- Crop Type Classification using
Satellite Images.- Fraud Detection using ML Algorithms.- Analysis of CNN
Models with Transfer Learning in Mango Diseases Detection.- Evaluating
Machine Learning Techniques for Student Performance Prediction in Higher
Education.- Threshold-Optimized Ensemble Learning for Accurate and Secure
Android Malware Detection.- Affective DDoS Attack Detection in EV Charging
Station using DL Autoencoder Model.- Federated Learning for
Privacy-Preserving Next- Word Prediction on Mobile Devices.- AI Based Plant
Health Monitoring under Stress Conditions.- Enhanced Weather Forecasting
using Random Forest, LSTM, Gradient Boosting and Ensemble Learning (RF+GB).-
Spatio-Temporal Analysis and Severity Prediction of Weather Events using
Machine Learning Models.- Image Deblurring using Generative Adversarial
Networks (GAN).- Triple-head Spatial Attention based Deep Learning Approach
for Plant Disease Identification.- Agent Based Analysis for Smart Traffic
Management.- Smart Solutions in Veterinary and Animal Sciences: Applications
of AI, ML and Soft Computing.- Helmet Mounted IoT based Physiological Health
Monitoring System for Soldiers.- Weather-Based Fault Detection in Solar Power
Generation by ML.- Advanced Price Forecasting for Food Commodities.- A
Practical and Explainable Network Anomaly Detection System for Enhanced
Cybersecurity.- Augmenting AI with Context: Hybrid Generative Models for
Summarizing Complex Medical Texts.- Detection and Classification of Cassava
Diseases using Concatenate Model.- AI based Solution for Smart Traffic
Management.- Effective Visualization Approaches for Distributed Denial of
Service Threat Prediction in Large-Scale Networks Using Interpretable Machine
Learning.- A Novel approach to integrate AI into Judicial Systems.- Energy
Efficiency in Software-Defined Wireless Network.- Enhanced Detection of
Distributed Denial-of-Service (DDoS) Attacks in Cloud Computing using
Transfer Learning, DBSCAN and Entropy Analysis.- Deep Transfer Learning with
GUI for Rice Pests Classification and Preventive Recommendations.- A Hybrid
Privacy-Preserving Framework for Cryptographic Efficiency in Vehicular Fog
Computing Networks.- Explainable Image Classification of Indian Butterflies
through Post-hoc Methods.- 5G Antenna Design Using Machine Learning
Algorithms.- Robust Hybrid Cryptographic Method for Cloud Computing
Information Security.- Advancing Water Quality Prediction: Integrating
Ensemble Learning and Explainable AI for Actionable Insights.- Predicting
Cryptocurrency Prices with Sentiment Analysis and Deep Learning Models.- RNN
and Logistic Regression-Based Ensemble Model for Distinguishing AI-Generated
Text.