Volume 1 of this three-part series introduces the fundamental concepts of quantum field theory using the formalism of canonical quantization. This volume is intended for use as a text for an introductory quantum field theory course that can include both particle and condensed matter physics students. Dr. Strickland starts with a brief review of classical field theory and uses this as a jumping off point for the quantization of classical field, thereby promoting them to proper quantum fields. He then presents the formalism for real and complex scalar field theories, fermion field quantization, gauge field quantization, toy models of the nuclear interaction, and finally the full Lagrangian for QED and its renormalization. Part of IOP Series in Nuclear Medicine.

We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's version of quantum mechanics. It has by now become fairly standard practice to refer to his theory as Bohmian mechanics and to the larger conceptual framework within which this is located as the causal quantum theory program. While it is true that one can have reservations about the appropriateness of these specific labels, both do elicit distinc tive images characteristic of the key concepts of these approaches and such terminology does serve effectively to contrast this class of theories with more standard formulations of quantum theory."

This book details groundbreaking experiments for the sensing and imaging of terahertz-frequency electromagnetic radiation (THz) using Rydberg atoms. The major advances described include the development and implementation of a new technique for THz imaging using atomic fluorescence; the demonstration of a THz-driven phase transition in room-temperature atomic vapour; and a novel method for probing the excited-state dynamics of atoms using quantum beats. The work has formed the basis for several articles published in journals including Nature Photonics and the Physical Review, and has sparked industry interest, becoming the subject of ongoing collaborative research and development. This exceptionally well-written book provides a definitive account of terahertz sensing with Rydberg atoms.

Given the extensive application of random walks in virtually every science related discipline, we may be at the threshold of yet another problem solving paradigm with the advent of quantum walks. Over the past decade, quantum walks have been explored for their non-intuitive dynamics, which may hold the key to radically new quantum algorithms. This growing interest has been paralleled by a flurry of research into how one can implement quantum walks in laboratories. This book presents numerous proposals as well as actual experiments for such a physical realization, underpinned by a wide range of quantum, classical and hybrid technologies.

The International Workshop on Quantum Communications and Measurement was held at the University of Nottingham from July 10-16, 1994. It followed the successful meeting on Quantum Aspects of Optical Communications in Paris in November 1990. This time the conference was devoted to mathematical, physical and engineering aspects of quantum noise, signal processing and quantum informa tion in open systems, quantum channels, and optical communications. It brought research workers in the experimental and engineering aspects of quantum optics and communication systems into contact with theoreticians working in quantum probability and measurement theory. The workshop was attended by more than 130 participants from 22 different countries. The largest groups after the UK (31)] were from Japan (19) and from Russia (14). The subjects discussed included the mathematical foundations of quantum communication systems, experiments and devices, the problem of collapse and continuous measurement, quantum input and output processes, causality and nondemolition observation, squeezed states, quan tum jumps, state diffusion and spontaneous localization, filtering and control in quantum systems, and new quantum optical phenomena and effects, including non classical light. These new mathematical and physical ideas were stimulated by recent advances in generation and detection of light with low quantum noise and the development of techniques for trapping a single atom over an extended period of time, making it possible to observe individual quantum phenomena at the macroscopic level."

Statistical Methods in Quantum Optics 2 - Non-Classical Fields continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in the first volume Statistical Methods in Quantum Optics 1 - Matter Equations and Fokker-Planck Equations the difficulties these methods face in treating non-classical light are exposed, where the regime of large fluctuations failure of the system size expansion is shown to be particularly problematic. Cavity QED is adopted as a natural vehicle for extending quantum noise theory into this regime. In response to the issues raised, the theory of quantum trajectories is presented as a universal approach to the treatment of fluctuations in open quantum systems.

This book presents its material at a level suitable for beginning researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems. The text is complemented by exercises and interspersed notes that point the reader to side issues or a deeper exploration of the material presented."

This thesis breaks new ground in the physics of photonic circuits for quantum optical applications. The photonic circuits are based either on ridge waveguides or photonic crystals, with embedded quantum dots providing the single qubit, quantum optical emitters. The highlight of the thesis is the first demonstration of a spin-photon interface using an all-waveguide geometry, a vital component of a quantum optical circuit, based on deterministic single photon emission from a single quantum dot. The work makes a further important contribution to the field by demonstrating the effects and limitations that inevitable disorder places on photon propagation in photonic crystal waveguides, a further key component of quantum optical circuits. Overall the thesis offers a number of highly novel contributions to the field; those on chip circuits may prove to be the only means of scaling up the highly promising quantum-dot-based quantum information technology.

Rob Clifton was one of the most brilliant and productive researchers in the foundations and philosophy of quantum theory, who died tragically at the age of 38. Jeremy Butterfield and Hans Halvorson collect fourteen of his finest papers here, drawn from the latter part of his career (1995-2002), all of which combine exciting philosophical discussion with rigorous mathematical results.
Many of these papers break wholly new ground, either conceptually or technically. Others resolve a vague controversy intoa precise technical problem, which is then solved; still others solve an open problem that had been in the air for soem time. All of them show scientific and philosophical creativity of a high order, genuinely among the very best work in the field.
The papers are grouped into four Parts. First come four papers about the modal interpretation of quantum mechanics. Part II comprises three papers on the foundations of algebraic quantum field theory, with an emphasis on entanglement and nonlocality. The two papers in Part III concern the concept of a particle in relativistic quantum theories. One paper analyses localization; the other analyses the Unruh effect (Rindler quanta) using the algebraic approach to quantum theory. Finally, Part IV contains striking new results about such central issues as complementarity, Bohr's reply to the EPR argument, and no hidden variables theorems; and ends with a philosophical survey of the field of quantum information. The volume includes a full bibliography of Clifton's publications.
Quantum Entanglements offers inspiration and substantial reward to graduates and professionals in the foundations of physics, with a background in philosophy, physics, or mathematics.

This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.

This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.

This book provides a comprehensive overview of the field of Higgs boson physics. It offers the first in-depth review of the complete results in connection with the discovery of the Higgs boson at CERN's Large Hadron Collider and based on the full dataset for the years 2011 to 2012. The fundamental concepts and principles of Higgs physics are introduced and the important searches prior to the advent of the Large Hadron Collider are briefly summarized. Lastly, the discovery and first mensuration of the observed particle in the course of the CMS experiment are discussed in detail and compared to the results obtained in the ATLAS experiment.

The rapid increase in capabilities at neutron and x-ray scattering sources has resulted in a wealth of highly accurate data on liquids, allowing for the testing of sophisticated models pertinent to the microscopic dynamics. This book, written with the experimentalist in the field of liquids in mind, is a practical guide on how to infer the maximum amount of information from the data using a minimum number of parameters, employing a fail-safe framework that ensures that pitfalls are avoided and that small differences between various liquids can be uncovered. Also, it details excitations for a range of liquids, covering simple fluids, colloids, mixtures, metals and superfluids. Results are interpreted in words rather than in equations, bringing to the fore new links between these fluids and between spontaneous fluctuations involving thousands of atoms down to those involving just a few. By providing a review of scattering results in the field of liquids, and placing various liquids in context, the book gives an overview for the graduate student and the postdoc entering the field, and a refresher course, based on modern results, for established experimentalists. Moreover, in re-establishing the connection between the large-scale properties of liquids, and their underlying collision sequences, the book directly ties experimental results to the most important open questions in the field. It is hoped that the book will inspire theorists to take up the challenges it poses.

With a minimum of mathematics, this book provides a novel approach to the teaching of quantum mechanics. As many books mainly present the concepts of quantum theory, this volume emphasises the application of the theory, offering the reader a unifying picture of atoms, molecules and solids. Essential for all undergraduate physics courses, it will also be a most valuable supplementary text for postgraduate courses on quantum mechanics.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Optically Polarized Atoms is addressed at upper-level undergraduate and graduate students involved in research in atomic, molecular, and optical Physics. It will also be useful to researchers practicing in this field. It gives an intuitive, yet sufficiently detailed and rigorous introduction to light-atom interactions with a particular emphasis on the symmetry aspects of the interaction, especially those associated with the angular momentum of atoms and light. The book will enable readers to carry out practical calculations on their own, and is richly illustrated with examples drawn from current research topics, such as resonant nonlinear magneto-optical effects. The book comes with a software package for a variety of atomic-physics calculations and further interactive examples that is freely downloadable from the book's web page, as well as additional materials (such as power-point presentations) available to instructors who adopt the text for their courses.

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin-Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

The purpose of this book is to initiate a new discipline, namely a formalized epistemological method drawn from the cognitive strategies practised in the most effective among the modern scientific disciplines, as well as from general philosophical thinking. Indeed, what is lacking in order to improve our knowledge and our domination of the modes which nowadays are available for the generation and communication of knowledge, thoroughly and rapidly and with precision and detail? It is a systematic explication of the epistemological essence encrypted in the specialized languages and algorithms of the major modern scientific approaches, a systematic cross-referencing of the explicated results, and a final elaboration of a new coherent whole.

Quantum mechanics, like a diver, can take us down to the level of the very first actions of our conceptualization of reality. And starting from there, it can induce an explicit understanding of certain fundamental features of the new scientific thinking.

A formalized epistemology should not be mistaken for a crossdisciplinary or a multidisciplinary project. The latter projects are designed to offer to nonspecialists access to information, to results obtained inside specialized disciplines, as well as a certain understanding of these results; whereas a formalized epistemology should equip anyone with a framework for conceptualizing himself in whatever domain and direction he or she might choose. A formalized epistemology should not be mistaken either for an approach belonging to the modern cognitive sciences. These try to establish as neutrally as possible descriptions of how the human body-and-mind work spontaneously when knowledge isgenerated; whereas a method of conceptualization should establish what conceptual-operational deliberate procedures have to be applied in order to represent and to achieve processes of generation of knowledge optimized accordingly to any definite aims.

This book addresses philosophers of science, physicists, mathematicians, logicians, computer scientists, researchers in cognitive sciences, and biologists, as well as any intellectual who is interested in scientific and philosophical thinking.

This thesis makes significant advances towards an understanding of superconductivity in the cuprate family of unconventional, high-temperature superconductors. Even though the high-temperature superconductors were discovered over 35 years ago, there is not yet a general consensus on an acceptable theory of superconductivity in these materials. One of the early proposals suggested that collective magnetic excitations of the conduction electrons could lead them to form pairs, which in turn condense to form the superconducting state at a critical temperature Tc. Quantitative calculations of Tc using experimental data were, however, not available to verify the applicability of this magnetic mechanism. In this thesis, the author constructed an angle-resolved photoemission apparatus that could provide sufficiently accurate data of the electronic excitation spectra of samples in the normal state, data which was furthermore unusually devoid of any surface contamination. The author also applied the Bethe-Salpeter method to his uncommonly pristine and precise normal state data, and was able to predict the approximate superconducting transition temperatures of different samples. This rare combination of experiment with sophisticated theoretical calculations leads to the conclusion that antiferromagnetic correlations are a viable candidate for the pairing interaction in the cuprate superconductors.

Modern nuclear physics is a well developed branch of physical science, with wide-ranging applications of its results in engineering and industry. At the same time, the development of a consistent theory of nuclei and nuclear processes presents certain problems. It is well known that the most important aim of nuclear physics is the study of nuclear structure and the explanation of properties on the basis of the interaction between nucleons which constitute nuclei. Difficulties of a modern theory of the nucleus are caused by both an insufficient knowledge of nuclear interactions and the multi particle character of nuclear systems. Experimental data on nuclear interactions do not contradict the hypothesis of the pair character of nuclear forces. However, the absence of rigorous meth ods of calculations of many particle nuclear systems with strong interaction makes it necessary to use macroscopic nuclear models to describe particular nuclear properties. Nuclear models have been developed in different ways, and the models themselves have been modified and complicated. In spite of the visible discrepancy, different models of the nucleus significantly supple ment one another. The development of nuclear models has led to considerable progress in the understanding of atomic nuclei. The current results of theo retical nuclear physics are reported in numerous scientific papers. The most important and relevant experimental and theoretical results can be found in many monographs, the best of which are written by well-known experts in the field."

This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are reviewed.

Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics.

This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.