This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as "loop quantum gravity", which gives rise to a quantization of space. In the second part the author introduces supersymmetry and its consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell's Theory as well as of Yang-Mills field theory, and of the standard model are worked out. Spontaneous symmetry breaking, improvement of the divergence problem in supersymmetric field theory, and its role in the hierarchy problem are covered. The unification of the fundamental constants in a supersymmetric version of the standard model are then studied. Geometrical aspects necessary to study supergravity are developed culminating in the derivation of its full action. The third part introduces string theory and the analysis of the spectra of the mass (squared) operator associated with the oscillating strings. The properties of the underlying fields, associated with massless particles, encountered in string theory are studied in some detail. Elements of compactification, duality and D-branes are given, as well of the generation of vertices and interactions of strings. In the final sections, the author shows how to recover GR and the Yang-Mills field Theory from string theory.

Quantum physics provides the concepts and their mathematical formalization that lend themselves to describe important properties of biological networks topology, such as vulnerability to external stress and their dynamic response to changing physiological conditions. A theory of networks enhanced with mathematical concepts and tools of quantum physics opens a new area of biological physics, the one of systems biological physics.

Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schroedinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.

This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.

This work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader 's disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches.

An understanding of the effects of electronic correlations in quantum systems is one of the most challenging problems in physics, partly due to the relevance in modern high technology. Yet there exist hardly any books on the subject which try to give a comprehensive overview on the field covering insulators, semiconductors, as well as metals. The present book tries to fill that gap.It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics. The reader will have a better understanding of the great progress which has been made in the field over the past few decades.

Choice Recommended Title, February 2020 This book explores quantum field theory using the Feynman functional and diagrammatic techniques as foundations to apply Quantum Field Theory to a broad range of topics in physics. This book will be of interest not only to condensed matter physicists but physicists in a range of disciplines as the techniques explored apply to high-energy as well as soft matter physics. Features: Comprehensive and rigorous, yet presents an easy to understand approach Applicable to a wide range of disciplines Accessible to those with little, or basic, mathematical understanding

With both industrial and teaching experience, the author explains the effects of time dependence in systems with two energy levels. The book starts with time-independent interactions and goes on to treat interactions with time-dependent electric and magnetic fields. Complete derivations are presented for each case, so the reader understands how the solutions are found. Both closed-form and numerical solutions are treated, and the calculations are compared with experimental data from the literature. Numerous plots are provided to show how the solutions depend on the parameters of the interactions.The book builds upon an undergraduate course in quantum mechanics and is useful for readers interested in magnetic resonance and quantum optics. In addition, this book is ideal for self-study by students or researchers starting on two-level systems. The detailed derivations and plots should ease readers into the study of two-level systems in a wide variety of settings.

This book describes the experimental and theoretical bases for the development of specifically quantum-mechanical approaches to metrology, imaging, and communication. In particular, it presents novel techniques developed over the last two decades and explicates them both theoretically and by reference to experiments which demonstrate their principles in practice. The particular techniques explored include two-photon interferometry, two-photon optical aberration and dispersion cancellation, lithography, microscopy, and cryptography.

This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Leon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.

Focusing on spectroscopic properties of molecular systems, Quantum Modeling of Molecular Materials presents the state-of-the-art methods in theoretical chemistry that are used to determine molecular properties relevant to different spectroscopies. This timely reference gives a basic presentation of response theory and its application to the simulation of spectroscopic properties of molecular materials. This in-depth presentation of time-dependent response theory and its applications in spectroscopy provides an important advance towards a modern vision of theoretical tools for researchers in academia and industry and postgraduate students.

Vladimir Naumovich Gribov is one of the creators of modern theoretical physics. The concepts and methods that Gribov has developed in the second half of the 20th century became cornerstones of the physics of high energy hadron interactions (relativistic theory of complex angular momenta, a notion of the vacuum pole - Pomeron, effective reggeon field theory), condensed matter physics (critical phenomena), neutrino oscillations, and nuclear physics.His unmatched insights into the nature of the quantum field theory helped to elucidate, in particular, the origin of classical solutions (instantons), quantum anomalies, specific problems in quantization of non-Abelian fields (Gribov anomalies, Gribov horizon), and the role of light quarks in the color confinement phenomenon.The fifth memorial workshop which marked Gribov's 85th birthday took place at the Landau Institute for Theoretical Physics, Russia, in June 2015. Participants of the workshop who came to Chernogolovka from different parts of the world presented new results of studies of many challenging theoretical physics problems across a broad variety of topics, and shared memories about their colleague, great teacher and friend.This book is a collection of the presented talks and contributed papers, which affirm the everlasting impact of Gribov's scientific heritage upon the physics of the 21st century.

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner ..". if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.

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.

The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles.

Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field.

This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

Several significant additions have been made to the second edition, including the operator method of calculating the bremsstrahlung cross-section, the calcualtion of the probabilities of photon-induced pair production and photon decay in a magnetic
field, the asymptotic form of the scattering amplitudes at high energies, inelastic scattering of electrons by hadrons, and the transformation of electron-positron pairs into hadrons.

After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.

Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Third Edition provides a complete course in quantum mechanics for students of semiconductor device physics and electrical engineering. It provides the necessary background to quantum theory for those starting work on micro- and nanoelectronic structures and is particularly useful for those beginning work with modern semiconductors devices, lasers, and qubits. This book was developed from a course the author has taught for many years with a style and order of presentation of material specifically designed for this audience. It introduces the main concepts of quantum mechanics which are important in everyday solid-state physics and electronics. Each topic includes examples which have been carefully chosen to draw upon relevant experimental research. It also includes problems with solutions to test understanding of theory. Full updated throughout, the third edition contains the latest developments, experiments, and device concepts, in addition to three fully revised chapters on operators and expectations and spin angular momentum, it contains completely new material on superconducting devices and approaches to quantum computing.

Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Third Edition provides a complete course in quantum mechanics for students of semiconductor device physics and electrical engineering. It provides the necessary background to quantum theory for those starting work on micro- and nanoelectronic structures and is particularly useful for those beginning work with modern semiconductors devices, lasers, and qubits. This book was developed from a course the author has taught for many years with a style and order of presentation of material specifically designed for this audience. It introduces the main concepts of quantum mechanics which are important in everyday solid-state physics and electronics. Each topic includes examples which have been carefully chosen to draw upon relevant experimental research. It also includes problems with solutions to test understanding of theory. Full updated throughout, the third edition contains the latest developments, experiments, and device concepts, in addition to three fully revised chapters on operators and expectations and spin angular momentum, it contains completely new material on superconducting devices and approaches to quantum computing.

This book reports on the search for a new heavy particle, the Vector-Like Top quark (VLT), in the Large Hadron Collider (LHC) at CERN. The signal process is the pair production of VLT decaying into a Higgs boson and top quark (TT Ht+X, X=Ht, Wb, Zt). The signal events result in top-antitop quarks final states with additional heavy flavour jets. The book summarises the analysis of the data collected with the ATLAS detector in 2015 and 2016. In order to better differentiate between signals and backgrounds, exclusive taggers of top quark and Higgs boson were developed and optimised for VLT signals. These efforts improved the sensitivity by roughly 30%, compared to the previous analysis. The analysis outcomes yield the strongest constraints on parameter space in various BSM theoretical models. In addition, the book addresses detector operation and the evaluation of tracking performance. These efforts are essential to properly collecting dense events and improving the accuracy of the reconstructed objects that are used for particle identification. As such, they represent a valuable contribution to data analysis in extremely dense environments.

This book addresses two disciplines that have traditionally occupied completely different realms: quantum information and computation, and game theory. Helping readers connect these fields, it appeals to a wide audience, including computer scientists, engineers, mathematicians, physicists, biologists or economists. The book is richly illustrated and basic concepts are accessible to readers with basic training in science. As such it is useful for undergraduate students as well as established academicians and researchers. Further, the didactic and tutorial-like style makes it ideal supplementary reading for courses on quantum information and computation, game theory, cellular automata and simulation.