This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.

This is an introductory book dealing with collective phenomena in many-body systems. A gas of bosons or fermions can show oscillations of various types of density. These are described by different combinations of field variables. Especially delicate is the competition of these variables. In superfluid 3He, for example, the atoms can be attracted to each other by molecular forces, whereas they are repelled from each other at short distance due to a hardcore repulsion. The attraction gives rise to Cooper pairs, and the repulsion is overcome by paramagnon oscillations. The combination is what finally led to the discovery of superfluidity in 3He. In general, the competition between various channels can most efficiently be studied by means of a classical version of the Hubbard-Stratonovich transformation.A gas of electrons is controlled by the interplay of plasma oscillations and pair formation. In a system of rod- or disc-like molecules, liquid crystals are observed with directional orientations that behave in unusual five-fold or seven-fold symmetry patterns. The existence of such a symmetry was postulated in 1975 by the author and K Maki. An aluminium material of this type was later manufactured by Dan Shechtman which won him the 2014 Nobel prize. The last chapter presents some solvable models, one of which was the first to illustrate the existence of broken supersymmetry in nuclei.

Besides classical applications (radar and stealth, antennas, microwave engineering), scattering and diffraction are enabling phenomena for some emerging research fields (artificial electromagnetic materials or metamaterials, terahertz technologies, electromagnetic aspects of nano-science). This book is a tutorial for advanced students who need to study diffraction theory. The textbook gives fundamental knowledge about scattering and diffraction of electromagnetic waves and provides some working examples of solutions for practical high-frequency scattering and diffraction problems.

The book focuses on the most important diffraction effects and mechanisms influencing the scattering process and describes efficient and physically justified simulation methods - physical optics (PO) and the physical theory of diffraction (PTD) - applicable in typical remote sensing scenarios.

The material is presented in a comprehensible and logical form, which relates the presented results to the basic principles of electromagnetic theory.

The book covers: basic definitions and equations (Maxwell's equations, boundary conditions, edge conditions, radiation conditions, radiation integral, scattering matrix and RCS); basic solution methods (separation of variables, Wiener-Hopf technique, Watson transformation, geometrical optics, geometrical theory of diffraction, physical optics, and physical theory of diffraction); solutions of Maxwell's equations for basic canonical geometries (a flat material interface, a circular cylinder, a sphere, a wedge, a half plane, a circular disc, an open-ended waveguide, and a cone) and their detailed analysis; explanations of fundamental scattering phenomena (edge and tip singularities, reflection from smoothly curved surfaces and flat non-metallic surfaces, edge-diffracted waves, creeping waves, multiply reflected / diffracted waves, surface waves, waveguide modes, tip-diffracted waves); a PTD-based approach for simulation of scattering and diffraction from generally shaped targets.

Causal Physics: Photons by Non Interactions of Waves redefines the mathematical Superposition Principle as an operational Superposition Effect; which is the measurable physical transformation experienced by a detector due to stimulations induced by multiple waves simultaneously acting on the detecting dipoles. This light-matter interaction process driven model emerges naturally by incorporating the observed properties, Non-Interaction of Waves (NIW) and quantized photo detectors needing to fill up their "quantum-cups" with the required quantity of energy from all the stimulating waves around it. By not incorporating this NIW-property explicitly, quantum mechanics failed to extract various embedded realities in the theory while incorporated unnecessary hypotheses like wave-particle duality. The book utilizes this NIW-property to explain all the major optical phenomena (diffraction, spectrometry, coherence.) without using any self-contradictory hypotheses that are prevalent now. The book redefines the old ether (constituting the space) as a stationary Complex Tension Field (CTF), holding all the energy of the universe (no need for Dark Energy of Dark Matter). CTF sustains perpetually propagating EM waves as its linear excitations and the particles as self-looped localized resonant non-linear excitations. Tensions are identified by Maxwell, then the velocities of emitting and detecting atoms through the CTF contribute to the Doppler shifts separately. This calls for re-visiting physical processes behind Hubble Redshift and hence Expanding Universe. The success of the book derives from a novel thinking strategy of visualizing the invisible interaction processes, named as Interaction Process Mapping Epistemology (IPM-E). This is over and above the prevailing strategy of Measurable Data Modeling Epistemology (MDM-E). The approach inspires the next generation of physicists to recognizing that the "foundation of the edifice of physics" has not yet been finalized. IPM-E will stimulate more of us to become technology innovators by learning to emulate the ontologically real physical processes in nature and become more evolution congruent. Critical thinkers without expertise in optical science and engineering, will appreciate the value of the content by reading the book backward, starting from Ch.12; which explains the critical thinking methodology besides giving a very brief summary of the contents in the previous chapters. Establishes that abandoning the wave-particle-duality actually allows us to extract more realities out of quantum mechanics. Illustrates how the discovery of the NIW-property profoundly impacts several branches of fundamental physics, including Doppler effect and hence the cosmological red shift Summarizes that many ad hoc hypotheses from physics can be removed, a la Occam's razor, while improving the reality and comprehension of some of the current working theories Demonstrates that our persistent attempts to restore causality in physical theories will be guided by our capability to visualize the invisible light matter interaction processes that are behind the emergence of all measurable data Draws close attention to the invisible but ontological interaction processes behind various optical phenomena so we can emulate them more efficiently and knowledgably in spite of limitations of our theories Designed as a reference book for general physics and philosophy, this optical science and engineering book is an ideal resource for optical engineers, physicists, and those working with modern optical equipment and high precision instrumentation.

Operational Quantum Theory I is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of these objects as the secondary focus is reversed with the operational interactions as basic quantum structures. Quantum theory, specifically nonrelativistic quantum mechanics, is developed from the theory of Lie group and Lie algebra operations acting on both finite and infinite dimensional vector spaces. In this book, time and space related finite dimensional representation structures and simple Lie operations, and as a non-relativistic application, the Kepler problem which has long fascinated quantum theorists, are dealt with in some detail. Operational Quantum Theory I features many structures which allow the reader to better understand the applications of operational quantum theory, and to provide conceptually appropriate descriptions of the subject. Operational Quantum Theory I aims to understand more deeply on an operational basis what one is working with in nonrelativistic quantum theory, but also suggests new approaches to the characteristic problems of quantum mechanics.

This thesis addresses the surprising features of zero-temperature statics and dynamics of several spin glass models, including correlations between soft spins that arise spontaneously during avalanches, and the discovery of localized states that involve the presence of two-level systems. It also presents the only detailed historiographical research on the spin glass theory. Despite the extreme simplicity of their definition, spin glasses display a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis the author sheds light on some of these, focusing on both the search for phase transitions under perturbations of Hamiltonians and the zero-temperature properties and responses to external stimuli. After introducing spin glasses and useful concepts on phase transitions and numerics, the results of two massive Monte Carlo campaigns on three-dimensional systems are presented: The first of these examines the de Almeida-Thouless transition, and proposes a new finite-size scaling ansatz, which accelerates the convergence to the thermodynamic limit. The second reconstructs the phase diagram of the Heisenberg spin glass with random exchange anisotropy.

This book is about the structure of multielectron atoms and predominantly adopts a perturbative approach to the total Hamiltonian. A key concept is the central-field approximation and, beyond the standard LS-coupling and jj-coupling schemes, intermediate cases are also treated. After that, the book covers hyperfine structure and other nuclear effects, as well as interactions with static external fields. Throughout the book, an analytical approach is adopted. Working knowledge of basic quantum mechanics (including the non-relativistic hydrogen atom, basic angular momentum and perturbation theory) is assumed, and it begins with a brief recap of the hydrogen orbitals, before turning towards the symmetry aspects of multi-electron atoms, spin-orbit interaction and couplings of angular momenta.

The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.

Modern physics is characterized by two great theories, which make it fundamentally different from its predecessor: quantum theory and theory of relativity. In this book we want to bring to the reader's attention several solutions to problems connected to the quantum-relativistic interaction of particles. Remarkably, such solutions furnished rigorous and pertinent explanations of a large set of phenomena, both in microscopic world and galactic universe.

We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.

We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.

This book provides an introduction to quantum theory primarily for students of mathematics. Although the approach is mainly traditional the discussion exploits ideas of linear algebra, and points out some of the mathematical subtleties of the theory. Amongst the less traditional topics are Bell's inequalities, coherent and squeezed states, and introductions to group representation theory. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group theoretical standpoint rather than the customary Lie algebraic approach. This book is intended for the later years of an undergraduate course or for graduates. It assumes a knowledge of basic linear algebra and elementary group theory, though for convenience these are also summarized in an appendix.

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.||Comments by distinguished physicists on "The Historical Development of Quantum Theory":||"¿the most definitive work undertaken by anyone on this vast and most important development in the history of physics. Jagdish Mehra, trained in theoretical physics under Pauli, Heisenberg, and Dirac, pursued the vision of his youth to write about the historical and conceptual development of quantum theory in the 20th century¿This series of books on the HDQT has thus become the most authentic and permanent source of our knowledge of how quantum theory, its extensions and applications developed. My heartfelt congratulations."|-Hans A. Bethe, Nobel Laureate||"A thrilling and magnificent achievement!"|-Subrahmanyan Chandrasekhar, FRS, Nobel Laureate||"¿capture(s) precisely, accurately, and thoroughly the very essence and all the fundamental details of the theory, and that is a remarkable achievement¿I have greatly enjoyed reading these books and learned so many new things from them. This series of books will remain a permanent source of knowledge about the creation and development of quantum theory. Congratulations!"|-Paul A. Dirac, FRS, Nobel Laureate||"The wealth and accuracy of detail in 'The Historical Development of Quantum Theory' are breathtaking."|-Richard P. Feynman, Nobel Laureate

Zeta regularization is a method to treat the divergent quantities appearing in several areas of mathematical physics and, in particular, in quantum field theory; it is based on the fascinating idea that a finite value can be ascribed to a formally divergent expression via analytic continuation with respect to a complex regulating parameter.This book provides a thorough overview of zeta regularization for the vacuum expectation values of the most relevant observables of a quantized, neutral scalar field in Minkowski spacetime; the field can be confined to a spatial domain, with suitable boundary conditions, and an external potential is possibly present. Zeta regularization is performed in this framework for both local and global observables, like the stress-energy tensor and the total energy; the analysis of their vacuum expectation values accounts for the Casimir physics of the system. The analytic continuation process required in this setting by zeta regularization is deeply linked to some integral kernels; these are determined by the fundamental elliptic operator appearing in the evolution equation for the quantum field. The book provides a systematic illustration of these connections, devised as a toolbox for explicit computations in specific configurations; many examples are presented. A comprehensive account is given of the existing literature on this subject, including the previous work of the authors.The book will be useful to anyone interested in a mathematically sound description of quantum vacuum effects, from graduate students to scientists working in this area.

Throughout their college career, most engineering students have done problems and studies that are basically situated in the classical world. Some may have taken quantum mechanics as their chosen field of study. This book moves beyond the basics to highlight the full quantum mechanical nature of the transport of carriers through nanoelectronic structures. The book is unique in that addresses quantum transport only in the materials that are of interest to microelectronics-semiconductors, with their variable densities and effective masses. The author develops Green's functions starting from equilibrium Green's functions and going through modern time-dependent approaches to non-equilibrium Green's functions, introduces relativistic bands for graphene and topological insulators and discusses the quantum transport changes that these bands induce, and discusses applications such as weak localization and phase breaking processes, resonant tunneling diodes, single-electron tunneling, and entanglement. Furthermore, he also explains modern ensemble Monte Carlo approaches to simulation of various approaches to quantum transport and the hydrodynamic approaches to quantum transport. All in all, the book describes all approaches to quantum transport in semiconductors, thus becoming an essential textbook for advanced graduate students in electrical engineering or physics.

This century has seen the development of technologies for manipulating and controlling matter and light at the level of individual photons and atoms, a realm in which physics is fully quantum-mechanical. The dominant experimental technology is the laser, and the theoretical paradigm is quantum optics.The Quantum World of Ultra-Cold Atoms and Light is a trilogy, which presents the quantum optics way of thinking and its applications to quantum devices. This book - 'Ultra-Cold Atoms' - provides a theoretical treatment of ultra-cold Bosons and Fermions and their interactions with electromagnetic fields in a form consistent with the first two books in the trilogy.The central concept is the quantum stochastic paradigm, formulated for cold collision physics. For Bosons, this yields a suite of techniques; versions of the stochastic Gross-Pitaevskii equation, using which a wide range of dynamic and thermal properties are formulated.The eBook editions of the 'Quantum World Trilogy' feature an extensive system of hyperlinks for ease of cross reference within the books, as well as links to the other books in the trilogy. In the section Viewing the eBooks we explain how these links work, and give some advice on appropriate pdf viewer applications.

Unravels Complex Problems through Quantum Monte Carlo Methods Clusters hold the key to our understanding of intermolecular forces and how these affect the physical properties of bulk condensed matter. They can be found in a multitude of important applications, including novel fuel materials, atmospheric chemistry, semiconductors, nanotechnology, and computational biology. Focusing on the class of weakly bound substances known as van derWaals clusters or complexes, Stochastic Simulations of Clusters: Quantum Methods in Flat and Curved Spaces presents advanced quantum simulation techniques for condensed matter. The book develops finite temperature statistical simulation tools and real-time algorithms for the exact solution of the Schroedinger equation. It draws on potential energy models to gain insight into the behavior of minima and transition states. Using Monte Carlo methods as well as ground state variational and diffusion Monte Carlo (DMC) simulations, the author explains how to obtain temperature and quantum effects. He also shows how the path integral approach enables the study of quantum effects at finite temperatures. To overcome timescale problems, this book supplies efficient and accurate methods, such as diagonalization techniques, differential geometry, the path integral method in statistical mechanics, and the DMC approach. Gleaning valuable information from recent research in this area, it presents special techniques for accelerating the convergence of quantum Monte Carlo methods.

* Which problems do arise within relativistic enhancements of the Schrodinger theory, especially if one adheres to the usual one-particle interpretation? * To what extent can these problems be overcome? * What is the physical necessity of quantum field theories? In many textbooks, only insufficient answers to these fundamental questions are provided by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this book emphasizes particularly this point of view (relativistic quantum mechanics in the ''narrow sense''): it extensively discusses the relativistic one-particle view and reveals its problems and limitations, therefore illustrating the necessity of quantized fields in a physically comprehensible way. The first two chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always with a view to the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the Feynman rules from propagator techniques. This is where the indispensability of quantum field theory reasoning becomes apparent and basic quantum field theory concepts are introduced. This textbook addresses undergraduate and graduate Physics students who are interested in a clearly arranged and structured presentation of relativistic quantum mechanics in the "narrow sense" and its connection to quantum field theories. Each section contains a short summary and exercises with solutions. A mathematical appendix rounds out this excellent textbook on relativistic quantum mechanics."

Features Covers both basic introductory topics, in addition to more advanced content Accompanied by over 200 problems starting from group algebra to the derivation of Migdal-Makeenko equations, Kim - Shifman - Vainshtein - Zakharov axion, and gluon + gluon to Higgs cross section, etc. Solutions are incorporated into the chapters to test understanding

The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion. Emphasizing a classical interpretation of quantum mechanics as developed by de Broeglie and Bohm, this volume: Introduces the concept of the quantum theory of motion Explains the connection with conventional quantum mechanics Presents various numerical techniques generated from the Bohmian approach Describes the epistemological significance of quantum trajectories Provides an authoritative account of the foundations of quantum mechanics vis-a-vis that of the Bohmian mechanics The popularity of using the quantum trajectory as a computational tool has exploded over the last decade, finally bringing this methodology to the level of practical applications. Many of the experts in the field who have either developed the methodology or have improved upon it have contributed chapters to this volume, making it a state-of-the-art expression of the field as it exists today and providing insight into the future of this technology.

Traditionally, new materials have been developed by empirically correlating their chemical composition, and the manufacturing processes used to form them, with their properties. Until recently, metallurgists have not used quantum theory for practical purposes. However, the development of modern density functional methods means that today, computational quantum mechanics can help engineers to identify and develop novel materials. Computational Quantum Mechanics for Materials Engineers describes new approaches to the modelling of disordered alloys that combine the most efficient quantum-level theories of random alloys with the most sophisticated numerical techniques to establish a theoretical insight into the electronic structure of complex materials such as stainless steels, Hume-Rothery alloys and silicates. The practical success of these approaches to applications in all of these areas are covered in detail.

In 1861, James Clerk-Maxwell published Part II of his four-part series 'On physical lines of force'. In it, he attempted to construct a vortex model of the magnetic field but after much effort neither he, nor other late nineteenth century physicists who followed him, managed to produce a workable theory. What survived from these attempts were Maxwell's four equations of electrodynamics together with the Lorentz force law, formulae that made no attempt to describe an underlying reality but stood only as a mathematical description of the observed phenomena. When the quantum of action was introduced by Planck in 1900 the difficulties that had faced Maxwell's generation were still unresolved. Since then theories of increasing mathematical complexity have been constructed to attempt to bring the totality of phenomena into order with little success. This work examines the problems that had been abandoned long before quantum mechanics was formulated in 1925 and argues that these issues need to be revisited before real progress in the quantum theory of the electromagnetic field can be made.

This book deals with quantum field theory, the language of modern elementary particles physics. Based on university lectures given by the author, this volume provides a detailed technical treatment of quantum field theory that is particularly useful for students; it begins with the quantization of the most important free fields, the scalar, the spin-1/2 and the photon fields, and is then followed by a detailed account of symmetry properties, including a discussion on global and local symmetries and the spontaneous breaking of symmetries. Perturbation theory, one-loop effects for quantum electrodynamics, and renormalization properties are also covered. In this second edition new chapters have been introduced with a general description of path integral quantization both on quantum mechanics and in quantum field theory, with a particular attention to the gauge fields. The path integral quantization of Fermi fields is also discussed.

This thesis presents the measurement of the Higgs boson cross section in the diphoton decay channel. The measurement relies on proton-proton collision data at a center-of-mass energy s = 13 TeV recorded by the ATLAS experiment at the Large Hadron Collider (LHC). The collected data correspond to the full Run-2 dataset with an integrated luminosity of 139 fb-1. The measured cross sections are used to constrain anomalous Higgs boson interactions in the Effective Field Theory (EFT) framework. The results presented in this thesis represent a reduction by a factor 2 of the different photon and jet energy scale and resolution systematic uncertainties with respect to the previous ATLAS publication. The thesis details the calibration of electron and photon energies in ATLAS, in particular the measurement of the presampler energy scale and the estimation of its systematic uncertainty. This calibration was used to perform a measurement of the Higgs boson mass in the H and H 4l channels using the 36 fb 1 dataset.

'Written by young theoretical physicists who are experts in the field, this volume is meant both to provide an introduction to the field and to offer a review of the latest developments, not discussed in many other existing books, for senior researchers. It will also appeal to scientists who do not work directly on LQG but are interested in issues at the interface of general relativity and quantum physics.'CERN CourierThis volume presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of younger leading researchers. It takes the reader from the basics to recent advances, thereby bridging an important gap.The aim is two-fold - to provide a contemporary introduction to the entire field for students and post-docs, and to present an overview of the current status for more senior researchers. The contributions include the latest developments that are not discussed in existing books, particularly recent advances in quantum dynamics both in the Hamiltonian and sum over histories approaches; and applications to cosmology of the early universe and to the quantum aspects of black holes.