The introduction of spin is believed to be a necessary tool if one wishes to quantize general relativity. Then the main problem is to see if the introduction of spin generalizing the general relativity from a geometric point of view, i.e. through the concept of torsion, can be experimentally verified.

The reader can find in this book both theoretical and experimental arguments which show the necessity for the introduction of spin, and then of torsion, in gravity. In fact, torsion constitutes the more natural and simple way to introduce spin in general relativity. For that reason it is of fundamental importance to see if there are some experiences that indicate -- if not directly, then at least indirectly -- the presence of torsion. This book presents a discussion on experiments with a polarized-mass torsion pendulum, the search for galactic dark matter interacting with a spin pendulum, a description of a space-based method for determination of the gravitational constant and space-based measurements of spin in gravity, as well as a discussion on theoretical arguments, for instance the nature of torsion and nonmetricity, the viability of gravitational theories with spin -- torsion and spin-spin interaction, many-dimensional gravitational theories with torsion, spinors on curved spaces, the spinors in real space -- time, etc.

We know that until now there has been no evidence for torsion, but this fact cannot prevent us from considering in some detail this implement of research that seems to be important from both a geometrical and a physical point of view.

Terahertz (THz) radiation with frequencies between 100 GHz and 30 THz has developed into an important tool of science and technology, with numerous applications in materials characterization, imaging, sensor technologies, and telecommunications. Recent progress in THz generation has provided ultrashort THz pulses with electric field amplitudes of up to several megavolts/cm. This development opens the new research field of nonlinear THz spectroscopy in which strong light-matter interactions are exploited to induce quantum excitations and/or charge transport and follow their nonequilibrium dynamics in time-resolved experiments. This book introduces methods of THz generation and nonlinear THz spectroscopy in a tutorial way, discusses the relevant theoretical concepts, and presents prototypical, experimental, and theoretical results in condensed matter physics. The potential of nonlinear THz spectroscopy is illustrated by recent research, including an overview of the relevant literature.

Emerging disciplines in the border zone between physics and chemistry have 1 attracted the attention of historians of science particularly in the last 20 years. 2 Quantum chemistry, as an offshoot of theoretical chemistry, has recently acquired 3 some importance in the history of chemistry. It is the product of close 1 Cf. Hiebert, E. : Discipline Identi cation in Chemistry and Physics, in: Science in Context, 9(2) (1996), 93-119; Nye, M. J. : Physics and Chemistry: Commensurate or Incommensurate Sciences? in: The Invention of Physical Science, Intersections of Mathematics, Theology and Natural Philosophy since the Seventeenth Century - Essays in Honor of Erwin N. Hiebert. Kluwer Academic Publishers, Dordrecht 1992; From Chemical Philosophy to Theoretical Chemistry: Dynamics of Matter and Dynamics of Disciplines, 1800-1950. University of California Press, Berkeley 1994; Servos, J. W. : Physical Chemistry from Ostwald to Pauling, the Making of a Science in America. Princeton University Press, New Jersey 1990; Chemical Sciences in the 20th Century: Bridging Boundaries, edited by Carsten Reinhard. Wiley-VCH, Weinheim 2001 (incl. a comprehensive bibliography). 2 In an earlier article I point out that the term "quantum chemistry" [Quantenchemie] rst appeared in 1929. To my knowledge it was coined by the physicist Arthur Haas. Talks he had del- ered before the Viennese Chemico-Physical Society in the spring of 1929 are assembled in his book: Die Grundlagen der Quantenchemie: Eine Einleitung in vier Vortrage. It was published by the Akademische Verlagsgesellschaft in Leipzig.

On June 19th 1999, the European Ministers of Education signed the Bologna Dec laration, with which they agreed that the European university education should be uniformized throughout Europe and based on the two cycle bachelor master's sys tem. The Institute for Theoretical Physics at Utrecht University quickly responded to this new challenge and created an international master's programme in Theoret ical Physics which started running in the summer of 2000. At present, the master's programme is a so called prestige master at Utrecht University, and it aims at train ing motivated students to become sophisticated researchers in theoretical physics. The programme is built on the philosophy that modern theoretical physics is guided by universal principles that can be applied to any sub?eld of physics. As a result, the basis of the master's programme consists of the obligatory courses Statistical Field Theory and Quantum Field Theory. These focus in particular on the general concepts of quantum ?eld theory, rather than on the wide variety of possible applica tions. These applications are left to optional courses that build upon the ?rm concep tual basis given in the obligatory courses. The subjects of these optional courses in clude, for instance, Strongly Correlated Electrons, Spintronics, Bose Einstein Con densation, The Standard Model, Cosmology, and String Theory.

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. The position fluctuations of the oscillator-a glass nanostring-are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg's uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object. The act of measurement not only perturbs the subject of the measurement-the mechanical oscillator-but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum - i.e., the light is squeezed. Lastly, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime, together with an exploration of the quantum limit of feedback control. The book offers a pedagogical account of linear measurement theory, its realization via optical interferometry, and contains a detailed guide to precision optical interferometry..

This thesis discusses in detail the measurement of the polarizations of all S-wave vector quarkonium states in LHC proton-proton collisions with the CMS detector. Heavy quarkonium states constitute an ideal laboratory to study non-perturbative effects of quantum chromodynamics and to understand how quarks bind into hadrons. The experimental results are interpreted through an original phenomenological approach, which leads to a coherent picture of quarkonium production cross sections and polarizations within a simple model, dominated by one single color-octet production mechanism. These findings provide new insights into the dynamics of heavy quarkonium production at the LHC, an important step towards a satisfactory understanding of hadron formation within the standard model of particle physics.

These lecture notes constitute a course on a number of central concepts of solid state physics - classification of solids, band theory, the developments in one-electron band theory in the presence of perturbation, effective Hamiltonian theory, elementary excitations and the various types of collective elementary excitation (excitons, spin waves and phonons), the Fermi liquid, ferromagnetic spin waves, antiferromagnetic spin waves and the theory of broken symmetry.The book can be used in conjunction with a survey course in solid state physics, or as the basis of a first graduate-level course. It can be read by anyone who has had basic grounding in quantum mechanics.

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

This book is a new edition of Volumes 3 and 4 of Walter Thirring's famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions. The author builds on an axiomatic basis and uses tools from functional analysis: bounded and unbounded operators on Hilbert space, operator algebras etc. Mathematics is shown to explain the axioms in depth and to provide the right tool for testing numerical data in experiments.

1bis text is meant to be a view of the quantum mechanical fonnalism as it develops with the successive introduction of different types oftransfonnations. In particular, it is meant to help the readers with three tasks: acquainting themselves with a general and direct approach to the quantum mechanics of spin one-half and spin-one particles, primarily leptons, photons and massive vector bosons, and to some extent quarks; finding out what some of the related areas of current research interest are; and, last and foremost, trying to understand the subject, beginning with and stressing the principles involved. The exposition is based on finite-dimensional representations of the homogeneous Lorentz group, and the subsequent introduction of gauge transformations, of the Abelian and non Abelian varieties. Reference to classical mechanics is avoided. Acting on the simple basis spinors and vectors, Lorentz transfonnations generate wave and field functions. Equations are obtained by the relativistic generalization of the addition of angular momenta, the wave or field functions being the solutions. For zero mass the equations may be obtained as the limits of the equations for the massive cases or by the application of the Euclidian group in two dimensions. The latter approach is illuminating in that it uncovers a loss in generality resulting from the former. Identifying momenta as eigenvalues of translations demonstrates covariance under the inhomogeneous Lorentz or Poincare group. Various representations of wave and field functions are given."

This thesis presents two production cross-section measurements of pairs of massive bosons using final states with leptons, made with the ATLAS detector at the Large Hadron Collider. The first measurement, performed using data collected in 2012 at center-of-mass energy s = 8 TeV, is the first fiducial and differential cross-section measurement of the production of the Higgs Boson when it decays to four charged leptons (electrons or muons). The second measurement is the first fiducial and inclusive production cross-section measurement of WZ pairs at center-of-mass energy s = 13 TeV using final states with three charged leptons. A significant portion of the thesis focuses on the methods used to identify electrons from massive boson decay-important for many flagship measurements-and on assessing the efficiency of these particle identification techniques. The chapter discussing the WZ pair cross-section measurement provides a detailed example of an estimate of lepton background in the context of an analysis with three leptons in the final state.

This subject is developed for readers with a fairly good knowledge of classical mechanics, electrodynamics and theory of relativity. The mathematics of linear vector spaces and matrices required is included as text and appendices. All principles and techniques are explained with illustrative applications. A Hilbert space formulation of the basic principles and the equations of motion are adopted at the outset. The treatment of linear vector spaces, matrices, angular momentum, relativistic wave equations, quantum field theory and the interpretational problem, is given in a more detailed way than in most books on quantum mechanics. Topics covered include Clebsch-Gordon and Racah coefficients, 9-j symbols and spherical tensors, the Klein-Gordon and the Weyl equations, Feynman's path-integral formalism, Feynman diagrams, Normal Products and Wick's Theorem, the EPR paradox, Hidden-variables theories and Bell's inequality. A number of problems are included with a view to supplementing the text. The present edition includes boundary value problems, representation theory, Fermi-Gas Model of the nuclei, Imaginary-mass Klein-Gordon equation, covariant and contravariant vectors, explanations of the EPR paradox and Einstein's concept of locality versus determinism.

n Angular Momentum Theory for Diatomic Molecules, R R method of trees, 3 construct the wave functions of more complicated systems for ex- ple many electron atoms or molecules. However, it was soon realized that unless the continuum is included, a set of hydrogenlike orbitals is not complete. To remedy this defect, Shull and Lowdin [273] - troduced sets of radial functions which could be expressed in terms of Laguerre polynomials multiplied by exponential factors. The sets were constructed in such a way as to be complete, i. e. any radial fu- tion obeying the appropriate boundary conditions could be expanded in terms of the Shull-Lowdin basis sets. Later Rotenberg [256, 257] gave the name "Sturmian" to basis sets of this type in order to emp- size their connection with Sturm-Liouville theory. There is a large and rapidly-growing literature on Sturmian basis functions; and selections from this literature are cited in the bibliography. In 1968, Goscinski [138] completed a study ofthe properties ofSt- rnian basis sets, formulating the problem in such a way as to make generalization of the concept very easy. In the present text, we shall follow Goscinski's easily generalizable definition of Sturmians.

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schroedinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell's inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

The first part of this third volume of Wigner's Collected Works is devoted to his analysis of symmetries in quantum mechanics, of the relativistic wave equations, of relativistic particle theory, and of field theory. It is introduced by the masterly annotation of Arthur S. Wightman. Abner Shimony annotates the second part where the reader will find Wigner's contributions to the foundations of quantum physics and to the problems of measurement.

This text builds a solid introduction to the concepts and techniques of quantum mechanics in settings where the phenomena treated are sufficiently simple that the student does not face two fundamental difficulties simultaneously: viz, that of learning quantum mechanics and that of learning how to assess the validity of models or the reliability of approximations. The treatment thus confines itself to systems that can either be solved exactly or be handled by well-controlled, plausible approximations. With few exceptions, this means systems with a small number of degrees of freedom. The exceptions are a first pass at many-electron atoms, the electromagnetic field, and the Dirac equation. (The inclusion of these last two topics reflects the now widely-held belief that every physicist should have at least a nodding acquaintance with these cornerstones of modern physics.) Born in Vienna, Kurt Gottfried emigrated to Canada in 1939 and received his Ph.D. in theoretical physics from MIT in 1955. He is professor of physics at Cornell University, and had previously been at Harvard University, the Massachusetts Institute of Technology, and at CERN in Geneva. He is the co-author of Concepts of Particle Physics (with V.F. Weisskopf), and of The Fallacy of Star Wars and Crisis, Stability, and Nuclear War. Gottfried has an active interest in arms control and human rights and is a founder and currently the Chair of the Union of Concerned Scientists.

From the Royal Society Winton Prize winner 'Sean Carroll examines what it means to exist on this speck of dust in a possibly infinite universe. It's fascinating to see a real working physicist thinking these things through and trying to come to a conclusion.' - Professor Brian Cox on The Big Picture, a Mail on Sunday Book of the Year Quantum physics is not mystifying. The implications are mind-bending, and not yet fully understood, but this revolutionary theory is truly illuminating. It stands as the best explanation of the fundamental nature of our world. Spanning the history of quantum discoveries, from Einstein and Bohr to the present day, Something Deeply Hidden is the essential guide to the most intriguing subject in science. Acclaimed physicist and writer Sean Carroll debunks the myths, resurrects and reinstates the Many-Worlds interpretation, and presents a new path towards solving the apparent conflict between quantum mechanics and Einstein's theory of general relativity. In doing so, he fills a gap in the science that has existed for almost a century. A magisterial tour, Something Deeply Hidden encompasses the cosmological and everyday implications of quantum reality and multiple universes. And - finally - it all makes sense.

This book describes the subject of electrodynamics at classical as well as quantum level, developed as an interaction at a distance. Thus it has electric charges interacting with one another directly and not through the medium of a field. In general such an interaction travels forward and backward in time symmetrically, thus apparently violating the principle of causality. It turns out, however, that in such a description the cosmological boundary conditions become very important. The theory therefore works only in a cosmology with the right boundary conditions; but when it does work it is free from the divergences that plague a quantum field theory.

This book describes the subject of electrodynamics at classical as well as quantum level, developed as an interaction at a distance. Thus it has electric charges interacting with one another directly and not through the medium of a field. In general such an interaction travels forward and backward in time symmetrically, thus apparently violating the principle of causality. It turns out, however, that in such a description the cosmological boundary conditions become very important. The theory therefore works only in a cosmology with the right boundary conditions; but when it does work it is free from the divergences that plague a quantum field theory.

In a distilled and pedagogical fashion, the contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. Further chapters deal with quantum gravity and D-brane geometry. Black hole mechanics and cosmology are treated too, as well as the AdS-CFT correspondence. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity. It addresses graduate students in physics and astrophysics.

The present book takes the discovery that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round on a fluid surface can also mimic the world of quantum mechanics. For the layman - for whom the main part of this book is written - this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works. The book is almost formula-free, and explains everything by using many sketches and diagrams. The mathematical derivations underlying the main text are kept separate in a -peer reviewed - appendix. The author, a retired professor of Flight Mechanics and Propulsion at the Delft University of Technology, chose to publish his findings in this mixed popular and scientific form, because he found that interested laymen more often than professional physicists feel the need to form visualisations of quantum phenomena.

In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

Revue sur la theorie des D-modules et modeles d'operateurs pseudodifferentiells, A Survey on the Theory of D-modules. Models for Pseudodifferential Operators.- Fourier Transform and Differential Equations.- Excursions and Ito Calculus in Nelson's Stochastic Mechanics.- Stark-Wannier Resonant States.- Spectral Properties of Adiabatically Perturbed Differential Operators with the Periodic Coefficients.- Quantum Tunnelling for Bloch Electrons in Small Electric Fields.- Asymptotic Invariant Subspaces; Abiabatic Theorems and Block Diagonalisation.- On the Quantum Hall-Effect.- Magnetic Schroedinger Operators and Effective Hamiltonians.- Perturbations of Supersymmetric Systems in Quantum Mechanics.- On the Eigenvalues of a Perturbed Harmonic Oscillator.- On Topics in Spectral and Stochastic Analysis for Schroedinger Operators.- Asymptotic Observables in the N-Body Quantum Long Range Scattering.- Spectral Properties of Bent Quantum Wires.- Eigenfunction Expansions for Hyperbolic Laplacians.- The Method of Differential Inequalities.- Supersymmetric Quantum Mechanics.- Propagation des singularites GEVREY pour la diffraction.- Reduction and Geometric Prequantization at the Cotangent Level.- Dirac Particles in Magnetic Fields.- On the Quasi-Stationary Approach to Scattering for Perturbations Periodic in Time.- Existence, Uniqueness and Some Properties of Schroedinger Propagators.

In this thesis the author discusses the phenomenology of supersymmetric models by means of experimental data set analysis of the electric dipole moment. There is an evaluation of the elementary processes contributing to the electric dipole moments within R-parity-violating supersymmetry, which call for higher-order perturbative computations.

A new method based on linear programming is developed and for the first time the non-trivial parameter space of R-parity violation respecting the constraints from existing experimental data of the electric dipole moment is revealed. As well, the impressive efficiency of the new method in scanning the parameter space of the R-parity-violating sector is effectively demonstrated. This new method makes it possible to extract from the experimental data a more reliable constraint on the R-parity violation.