Physics

Problems in Quantum Mechanics and Field Theory with Mathematical Modelling

Aleksander V. Chichurin, Elena M. Ovsiyuk, Viktor M. Red’kov

In Problems in Quantum Mechanics and Field Theory with Mathematical Modelling, a number of exactly solvable problems in electrodynamics and in quantum-mechanics of particles with different spins are presented. The main topics covered the Cox scalar particle with intrinsic structure in presence of the magnetic field in the spaces of constant curvature, Euclid, Riemann, and Lobachevsky; Cox particle in the Coulomb field; tunneling effect through Schwarzschild barrier for a spin 1/2 particle; electromagnetic field in Schwarzschild space-time, the Majorana - Oppenheimer approach in electrodynamics; scalar particle with polarizability in the Coulomb field; Dirac particle in the Coulomb field on the background of hyperbolic Lobachevsky and spherical Riemann models; particle with spin 1 in the Coulomb field; geometrical modeling of the media in Maxwell electrodynamics; P-asymmetric equation for a spin 1/2 particle; fermion with two mass parameters in the Coulomb field; helicity operator for a spin 2 particle in presence of the magnetic field. The book will be of interest to researchers, and is accessible enough to serve as a self-study resources for courses at undergraduate and graduate levels.

Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit

Prof W. M. Stuckey, Prof Michael Silberstein, Dr Timothy McDevitt

Existential Physics: A Scientist's Guide to Life's Biggest Questions

Sabine Hossenfelder

"A contrarian scientist wrestles with the big questions that modern physics raises, and what physics says about the human condition Not only can we not currently explain the origin of the universe, it is questionable we will ever be able to explain it. The notion that there are universes within particles, or that particles are conscious, is ascientific, as is the hypothesis that our universe is a computer simulation. On the other hand, the idea that the universe itself is conscious is difficult to rule out entirely. According to Sabine Hossenfelder, it is not a coincidence that quantum entanglement and vacuum energy have become the go-to explanations of alternative healers, or that people believe their deceased grandmother is still alive because of quantum mechanics. Science and religion have the same roots, and they still tackle some of the same questions: Where do we come from? Where do we go to? How much can we know? The area of science that is closest to answering these questions is physics. Over the last century, physicists have learned a lot about which spiritual ideas are still compatible with the laws of nature. Not always, though, have they stayed on the scientific side of the debate. In this lively, thought-provoking book, Hossenfelder takes on the biggest questions in physics: Does the past still exist? Do particles think? Was the universe made for us? Has physics ruled out free will? Will we ever have a theory of everything? She lays out how far physicists are on the way to answering these questions, where the current limits are, and what questions might well remain unanswerable forever. Her book offers a no-nonsense yet entertaining take on some of the toughest riddles in existence, and will give the reader a solid grasp on what we know-and what we don't know"

Compact Objects in the Universe

Eleftherios Papantonopoulos, Mavromatos Nikolaos

The main objective of this volume is to discuss the physical properties, observational signals and various probes of compact objects in the Universe. These include black holes, neutron stars, and exotic objects studied in alternative theories of gravity. The text is mainly addressed to postgraduate students and young researchers with the aim of introducing them to these very challenging topics.

Compact Objects in the Universe

Eleftherios Papantonopoulos, Nikolaos Mavromatos

The main objective of this volume is to discuss the physical properties, observational signals and various probes of compact objects in the Universe. These include black holes, neutron stars, and exotic objects studied in alternative theories of gravity. The text is mainly addressed to postgraduate students and young researchers with the aim of introducing them to these very challenging topics.

Random Walks and Physical Fields

Yves Le Jan

Old Quantum Theory and Early Quantum Mechanics: A Historical Perspective Commented for the Inquiring Reader

Marco Giliberti, Luisa Lovisetti

This book provides a historical presentation of Old Quantum Theory and early Quantum Mechanics integrated with comments and examples that help contextualize and understand the physics discussed. It consists in a detailed analysis of the usual topics that have most contributed to the birth and the development of Quantum Mechanics (black-body spectrum, atomic models, EPR paradox, etc.), but also dealing with ideas, concepts and results that are not usually treated (vortex atoms, discussion on the meaning of the term “electron”, non-quantum models of the Compton effect, etc.). The time span taken into consideration goes mainly from the 1880s to the 1940s; but some brief notes on more recent results are also presented in the appendixes. The work is based on nearly 800 original documents – books, papers, letters, newspapers – whose content is not only partially reported, but also explained, and inserted in the historical, social and disciplinary context of the time. Together with a rigorous historical framework, the book offers also an educational discussion of the physical aspects presented. Indeed, there are some specific sections and subsections with pedagogical observations. This book is intended for students pursuing STEM degrees, particularly those seeking an understanding of the genesis and rationale behind quantum mechanics. But it is surely also addressed to professional physicists who are eager to reconsider the cultural foundations underlying the quantum view of the world. We are thus thinking of inquiring minds, people who teach quantum physics, and individuals involved in quantum technologies.

Statistical Mechanics of Phases and Phase Transitions

Steven A Kivelson, Jack Mingde Jiang, Jeffrey Chang

An engaging undergraduate introduction to the statistical mechanics of phase transitions Statistical mechanics deploys a powerful set of mathematical approaches for studying the thermodynamic properties of complex physical systems. This textbook introduces students to the statistical mechanics of systems undergoing changes of state, focusing on the basic principles for classifying distinct thermodynamic phases and the critical phenomena associated with transitions between them. Uniquely designed to promote active learning, Statistical Mechanics of Phases and Phase Transitions presents some of the most beautiful and profound concepts in physics, enabling students to obtain an essential understanding of a computationally challenging subject without getting lost in the details.

Free Boundary Problems in Fluid Dynamics

Albert Ai, Thomas Alazard, Mihaela Ifrim, Daniel Tataru

Escape from Shadow Physics: The Quest to End the Dark Ages of Quantum Theory

Adam Forrest Kay

An expert physicist argues for a revolutionary new understanding of quantum mechanics. The received wisdom in quantum physics is that, at the deepest levels of reality, there are no actual causes for atomic events. This idea led to the outlandish belief that quantum objects — indeed, reality itself — aren’t real unless shaped by human measurement. Einstein mocked this idea, asking whether his bed spread out across his room unless he looked at it. And yet it remains one of the most influential ideas in science and our culture. In Escape from Shadow Physics, Adam Forrest Kay takes up Einstein’s torch: reality isn’t mysterious or dependent on human measurement, but predictable and independent of us. At the heart of his argument is groundbreaking research with little drops of oil. These droplets behave as particles do in the long-overlooked quantum theory of pilot waves; crucially, they showcase quantum behavior while being described by classical physics. What if the original doubters of our quantum orthodoxy (not least Einstein himself) were onto something? What if pilot wave theory was right all along? In that case, our whole story of twentieth-century physics is topsy-turvy, and we must give up the idea that reality is simply too weird to grasp. Weird it may still be, but a true understanding of nature now seems within our reach.

Introduction to Topological Quantum Matter & Quantum Computation

Tudor D Stanescu

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.

Quantum Mechanics for Material Science: An Introduction

Gianluca Stefanucci

This book is based on the course "Elements of Theoretical Physics," which the author has been teaching at the University of Rome Tor Vergata since 2017. It serves as an introduction to quantum mechanics, providing students with essential concepts and tools for future lessons, while still maintaining a comprehensive approach without relying heavily on the level of abstraction and mathematical rigor typically found in Physics programs. Understanding this book only requires knowledge of the mathematical concepts taught in the first two years of basic courses. The bachelor's degree program in Materials Science aims to train students with an interdisciplinary background in physics, chemistry, and engineering. While the study of quantum mechanics is essential, the same level of depth, abstraction, and mathematical rigor as in a Physics degree program is not a requirement. Unfortunately, most textbooks on Quantum Mechanics are geared toward Physics students, making it difficult to find suitable resources for Materials Science students. To make learning easier, the author has chosen not to refer students to various textbooks for different topics. Instead, he has created handouts that have evolved into a condensed textbook on quantum mechanics specifically tailored to the needs of the Materials Science program.

Lagrangian and Hamiltonian Mechanics: A Modern Approach with Core Principles and Underlying Topics

José Rachid Mohallem

Interpreting Quantum Mechanics: Modern Foundations

David W. Snoke

This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins by introducing some of the more controversial topics in the foundations of quantum mechanics, with only very basic mathematics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensure the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and philosophy of science interested in the foundations of quantum mechanics.

Color in QCD: An Introduction Featuring the Birdtrack Pictorial Technique

Stéphane Peigné

This book introduces readers to the fascinating world of quantum chromodynamics (QCD) and quarks and gluons, the elementary constituents of protons, neutrons, and all hadrons. Specifically, it focuses on the color of quarks and gluons, responsible for their mutual interactions via the strong force.  The book provides an elementary introduction to the birdtrack technique, which is a powerful tool for addressing the color structure of QCD in a pictorial way. The technique shows how quark and gluon colors are combined and mixed in QCD. The author discusses color conservation, shows how to project on color states of systems of quarks, antiquarks, and gluons, how to derive their color charges. The book is enriched with many exercises integrated in the text to learn by doing. This book is primarily intended for particle physics students, graduates, and researchers working in the field of QCD. However, it requires no specific prerequisites in QCD, so it may also be of interest to students of mathematics, as an illustration of the use of the birdtrack pictorial technique in representation theory.

Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory

Paul-Hermann Balduf

This book offers a systematic introduction to the Hopf algebra of renormalization in quantum field theory, with a special focus on physical motivation, the role of Dyson–Schwinger equations, and the renormalization group. All necessary physical and mathematical constructions are reviewed and motivated in a self-contained introduction. The main part of the book concerns the interplay between Dyson–Schwinger equations (DSEs) and renormalization conditions. The book is explicit and consistent about whether a statement is true in general or only in particular renormalization schemes or approximations and about the dependence of quantities on regularization parameters or coupling constants. With over 600 references, the original literature is cited whenever possible and the book contains numerous references to other works discussing further details, generalizations, or alternative approaches. There are explicit examples and remarks to make the connection from the scalar fields at hand to QED and QCD. The book is primarily targeted at the mathematically oriented physicist who seeks a systematic conceptual overview of renormalization, Hopf algebra, and DSEs. These may be graduate students entering the field as well as practitioners seeking a self-contained account of the Hopf algebra construction. Conversely, the book also benefits the mathematician who is interested in the physical background of the exciting interplay between Hopf algebra, combinatorics and physics that is renormalization theory today.

Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory

Paul-Hermann Balduf

This book offers a systematic introduction to the Hopf algebra of renormalization in quantum field theory, with a special focus on physical motivation, the role of Dyson–Schwinger equations, and the renormalization group. All necessary physical and mathematical constructions are reviewed and motivated in a self-contained introduction. The main part of the book concerns the interplay between Dyson–Schwinger equations (DSEs) and renormalization conditions. The book is explicit and consistent about whether a statement is true in general or only in particular renormalization schemes or approximations and about the dependence of quantities on regularization parameters or coupling constants. With over 600 references, the original literature is cited whenever possible and the book contains numerous references to other works discussing further details, generalizations, or alternative approaches. There are explicit examples and remarks to make the connection from the scalar fields at hand toQED and QCD. The book is primarily targeted at the mathematically oriented physicist who seeks a systematic conceptual overview of renormalization, Hopf algebra, and DSEs. These may be graduate students entering the field as well as practitioners seeking a self-contained account of the Hopf algebra construction. Conversely, the book also benefits the mathematician who is interested in the physical background of the exciting interplay between Hopf algebra, combinatorics and physics that is renormalization theory today.

BRST Symmetry and de Rham Cohomology

Soon-Tae Hong

This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization for constrained physical systems and its corresponding de Rham cohomology group structure. These were studied by theoretical physicists from the early 1960s and appeared in attempts to quantize rigorously some physical theories such as solitons and other models subject to geometrical constraints. In particular, phenomenological soliton theories such as Skyrmion and chiral bag models have seen a revival following experimental data from the SAMPLE and HAPPEX Collaborations and these are discussed. The book describes how these model predictions were shown to include rigorous treatments of geometrical constraints because these constraints affect the predictions themselves. The application of the BRST symmetry to the de Rham cohomology contributes to a deep understanding of Hilbert space of constrained physical theories. Aimed at graduate-level students in quantum field theory, the book will also serve as a useful reference for those working in the field.  An extensive bibliography guides the reader towards the source literature on particular topics.

Classical Double Copy, The: New Connections In Gauge Theory And Gravity

Christopher White

Quantum Geometry, Matrix Theory, and Gravity

Harold C. Steinacker

Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang–Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.

Introduction to Quantum Mechanics: With a Focus on Physics and Operator Theory

Horst R. Beyer

This book presents an introduction to quantum mechanics that consistently uses the methods of operator theory, allowing readers to develop a physical understanding of quantum mechanical systems. The methods of operator theory are discussed throughout the book and presented with a mathematically rigorous approach. The author describes in detail how to use the methods of operator theory for analyzing quantum mechanical systems, starting with the definition of the involved physical operators (observables) up to the calculation of their spectra, spectral measures, and functional calculus. In addition, the book includes the construction of exponential functions of the involved Hamilton operators that solve the problem of time evolution.

Quantum Mechanics: An Accessible Introduction

Robert J Scherrer

Matrix Models for Population, Disease, and Evolutionary Dynamics

J. M. Cushing

Classical Mechanics and Relativity

Harald J.W. Müller-Kirsten

Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology

Paul Benioff, Marek Czachor

The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

Steven H Strogatz

Mueller-Matrix Tomography of Biological Tissues and Fluids: Digital Image Processing and Analysis Techniques

Zhengbing Hu, Iryna V. Soltys, Alexander V. Dubolazov, Liliya Yu. Trifonyuk, M.P. Gorsky, Oleksandr V. Olar

This book presents experimental investigations and digital image processing, highlighting the interaction of polarized radiation with phase-inhomogeneous and optically anisotropic biological layers. The promising and efficient use of vector-parametric description of the formation of polarization-inhomogeneous object fields is noted. Applications of a set of Mueller-matrix polarimetry methods are highlighted. The book includes- structural and logical scheme of multi-parameter (singular, interference and layer-by-layer Stokes-polarimetric), polarization-correlation study of the structure of distributions of the number of singularities, maps of local contrast of interference distributions and layer-by-layer maps of microscopic polarization azimuth and ellipticity; determination of relationships between changes in the magnitude of statistical parameters characterizing polarization-correlation distributions and pathology of prostate tumors.

Characterizing Multiparticle Entanglement Using the Schmidt Decomposition of Operators

Sophia Denker

Characterizing entanglement is an important issue in quantum information, as it is considered to be a resource for many applications such as quantum key distribution or quantum metrology. One useful tool to detect and quantify entanglement are witness operators. A standard way to construct them is based on the fidelity of pure states and mathematically relies on the Schmidt decomposition of vectors. In this book a method to build entanglement witnesses using the Schmidt decomposition of operators is presented. One can show that these are strictly stronger than the fidelity witnesses. Moreover, the concept can be generalized easily to the multipartite case, and one may use it to quantify the dimensionality of entanglement. Finally, this scheme will be used to provide two algorithms that can be combined to improve given witnesses for multiparticle entanglement.

Sbornik zadach po elem.fizike: Posob.dlya samoobr.

Buhovcev Boris Borisovich; Myakishev G. YA.; Krivchenkov V. D.

Trails in Modern Theoretical and Mathematical Physics: A Volume in Tribute to Giovanni Morchio

Andrea Cintio, Alessandro Michelangeli

This book celebrates the life and work of the late Giovanni Morchio (1944–2021). It features scientific and anecdotal contributions written by his former colleagues, co-authors, and students, as well as senior scientists who were active witnesses to the dramatic advances in physics and in mathematics that took place during his 50-year-long career. The volume begins with a biographical introduction, detailing Giovanni Morchio’s life and his role as a physicist, mathematician, teacher, and scientist. The core of the book covers a vast spectrum of ideas, reflecting Dr Morchio’s scientific interests. Each chapter develops a specific topic of modern research, ranging from quantum mechanics and quantum field theory to additional themes such as the connection between general relativity and Newtonian gravitation. Every contribution provides a historical retrospective, a survey of advances, an outlook of future perspectives and challenges, and an updated bibliography. The last part collects the authors’ recollections of their professional and personal interactions with Dr Morchio, in recognition of his deep achievements, his exceptional pedagogical qualities, and his praiseworthy social and pro bono commitment. Authored by physicists of international calibre covering a broad range of subjects, the book will be a valuable reference for researchers and students of theoretical and mathematical physics.