Theory of interacting quantum fields
Rebenko, Alexei L
2012-01-01
This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.
Wilczek, Frank
1998-01-01
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. I mention a few of its most striking successes, both achieved and prospective. Possible limitations of quantum field theory are viewed in the light of its history.
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
Mandl, Franz
2010-01-01
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic
Euclidean Relativistic Quantum Mechanics
Kopp, Philip; Polyzou, Wayne
2013-01-01
We discuss a formulation of exactly Poincar\\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction and transformation properties of single-particle states, and the construction of GeV scale transition matrix elements. A simple model is utilized to demonstrate the feasibility of this approach.
Zeidler, Eberhard
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Statistical approach to quantum field theory an introduction
Wipf, Andreas
2013-01-01
Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems w...
Digestible quantum field theory
Smilga, Andrei
2017-01-01
This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven‐course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious “extras” in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrées ‐ the central par t of the book where the...
Studies in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Bender, C.M.; Mandula, J.E.; Shrauner, J.E.
1982-03-05
Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD.
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
Lectures on quantum field theory
Das, Ashok
2008-01-01
This book consists of the lectures for a two-semester course on quantum field theory, and as such is presented in a quite informal and personal manner. The course starts with relativistic one-particle systems, and develops the basics of quantum field theory with an analysis of the representations of the Poincaré group. Canonical quantization is carried out for scalar, fermion, Abelian and non-Abelian gauge theories. Covariant quantization of gauge theories is also carried out with a detailed description of the BRST symmetry. The Higgs phenomenon and the standard model of electroweak interactio
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
Quantum field theory and critical phenomena
Zinn-Justin, Jean
1996-01-01
Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics. This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and the renormalization group are examined, as are critical phenomena and the role of instantons. Changes for this edition 1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing. 2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic li...
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum Field Theory, Revised Edition
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Introduction to quantum field theory
Chang, Shau-Jin
1990-01-01
This book presents in a short volume the basics of quantum field theory and many body physics. The first part introduces the perturbative techniques without sophisticated apparatus and applies them to numerous problems including quantum electrodynamics (renormalization), Fermi and Bose gases, the Brueckner theory of nuclear system, liquid Helium and classical systems with noise. The material is clear, illustrative and the important points are stressed to help the reader get the understanding of what is crucial without overwhelming him with unnecessary detours or comments. The material in the s
Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
Barvinsky, A O
2015-01-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter stage of cosmological evolution at an arbitrary value of $\\varLambda$ -- a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scala...
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
A philosophical approach to quantum field theory
Öttinger, Hans Christian
2017-01-01
This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.
Statistical approach to quantum field theory. An introduction
Energy Technology Data Exchange (ETDEWEB)
Wipf, Andreas [Jena Univ. (Germany). Theoretisch-Physikalisches Inst.
2013-02-01
Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate
Numerical calculations in quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Rebbi, C.
1984-01-01
Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references. (WHK)
Linking topological quantum field theory and nonperturbative quantum gravity
Smolin, Lee
1995-11-01
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the pullback of the curvature to the boundary is self-dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern-Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern-Simons theory is found to be given by k=6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. Given these results, it is natural to make the conjecture that the quantum states of the system are completely determined by measurements made on the boundary. One consequence of this is the Bekenstein bound, which says that once the two metric of the boundary has been measured, the subspace of the physical state space that describes the further information that may be obtained about the interior has finite dimension equal to the exponent of the area of the boundary, in Planck units, times a fixed constant. Finally, these results confirm both the categorical-theoretic ``ladder of dimensions'' picture of Crane and the holographic hypothesis of Susskind and 't Hooft.
Quantum and Thermal Fluctuations in Field Theory
Liao, Sen-Ben; Polonyi, Janos; Xu, Dapeng
1994-01-01
Blocking transformation is performed in quantum field theory at finite temperature. It is found that the manner temperature deforms the renormalized trajectories can be used to understand better the role played by the quantum fluctuations. In particular, it is conjectured that domain formation and mass parameter generation can be observed in theories without spontaneous symmetry breaking.
The conceptual basis of Quantum Field Theory
Hooft, G. 't
2005-01-01
Relativistic Quantum Field Theory is a mathematical scheme to describe the sub-atomic particles and forces. The basic starting point is that the axioms of Special Relativity on the one hand and those of Quantum Mechanics on the other, should be combined into one theory. The fundamental
Quantum Field Theory in a Semiotic Perspective
Günter Dosch, Hans; Sieroka, Norman
2005-01-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
Quantum Field Theory with Varying Couplings
Calcagni, Gianluca; Nardelli, Giuseppe
2014-01-01
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories.
Mathematical aspects of quantum field theory
de Faria, Edson
2010-01-01
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Studies in quantum field theory. Progress report
Energy Technology Data Exchange (ETDEWEB)
Bender, C.M.; Shrauner, J.E.; Mandula, J.E.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, l/N expansions, quantum solitons, phase transitions, and nuclear potentials. Progress is reported. (WHK)
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
The conceptual framework of quantum field theory
Duncan, Anthony
2012-01-01
The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quan...
Quantum field theory and the standard model
Schwartz, Matthew D
2014-01-01
Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the-art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independe...
An introduction to relativistic quantum field theory
Schweber, Silvan S
1961-01-01
Complete, systematic, and self-contained, this text introduces modern quantum field theory. "Combines thorough knowledge with a high degree of didactic ability and a delightful style." - Mathematical Reviews. 1961 edition.
Circuit complexity in quantum field theory
Jefferson, Robert A.; Myers, Robert C.
2017-10-01
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities.
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which 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 first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Physical properties of quantum field theory measures
Mourão, J. M.; Thiemann, T.; Velhinho, J. M.
1999-05-01
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.
Towards the mathematics of quantum field theory
Paugam, Frédéric
2014-01-01
The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second...
Wilson lines in quantum field theory
Cherednikov, Igor O; Veken, Frederik F van der
2014-01-01
The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. It teaches how to perform independently with some elementary calculations on Wilson lines, and shows the recent development of the subject in different important areas of research.
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Reconditioning in Discrete Quantum Field Theory
Gudder, S.
2017-12-01
We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S( x 0, r) where x 0 and r are positive integers representing time and maximal total energy, respectively. The operator S( x 0, r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy ( x 0, r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each ( x 0, r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.
Quantum field theory in curved spacetime
Castagnino, M
1993-01-01
When we began to study, in the seventies, Quantum Field Theory in Curved Space time (QFTCST), we thought that WV were count Hu'ling a fundnnu-Jltul llu‘m'y. r‘n-‘mn— passing General Relativity and Quantum Field 'l‘lum)‘ ((Ql'ﬁrlﬂt lt was soon evident that QFTCST is only the ixl'lilif‘lilhr-ilt‘fll :i]nprmunmtinn to (Quantum (iiraviiy {QC} :1 yet unknown thery. After ‘20 years, normally a physical theory, it it is not fundamen- tal, decays and dies. On the contrary, QFTCH'I‘ is wry much alive, as it is pi‘ln'ml by the almost 50 abstracts submitted to this workshop, This is so because many people are trying to define and develope QFTCST in very interesting and important cases, such as Gott’s space or non globally hyperbolic spaces etc. (as we shall see in section 1), because QFTCST is useful to study the quantum nature of Black Holes (BH) (as we shall see in section 2) and because this fm‘nialism is an esential tool for Quantum Cosmology; like in inflationary models (as we shall se...
Quantum Algorithms for Fermionic Quantum Field Theories
2014-04-28
Feynman rules for the discretized theory. The propagator is = γµp̃µ + m̃(p) p̃2 − m̃(p)2 , (120) where p̃µ... Feynman rules are = −i , = −ig . (124) At one-loop order, − iM(p) = + , (125) where the second diagram is the counterterm. The first diagram gives = −g20...stabilizer problem, arXiv:quant-ph (1995). [37] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma, Exponential improvement in precision for simulating sparse Hamiltonians, arXiv:1312.1414 (2013). 29
Superconformal quantum field theory in curved spacetime
de Medeiros, Paul; Hollands, Stefan
2013-09-01
By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.
The Boltzmann equation from quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Drewes, Marco, E-mail: marco.drewes@tum.de [Institut fuer Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, 52056 Aachen (Germany); Physik Department T70, Technische Universitaet Muenchen, James Franck Strasse 1, D-85748 Garching (Germany); Mendizabal, Sebastian [Institut fuer Theoretische Physik, Goethe-Universitaet, 60438 Frankfurt am Main (Germany); Weniger, Christoph [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2013-01-08
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
Quantum processes: A Whiteheadian interpretation of quantum field theory
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Quantum field theory and the internal states of elementary particles
CSIR Research Space (South Africa)
Greben, JM
2011-01-01
Full Text Available A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent fields...
Cosmological horizons and reconstruction of quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, C.; Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Trento Univ., Povo (Italy). Istituto Nazionale di Alta Matematica ' ' F. Severi' ' - GNFM; Moretti, V. [Trento Univ. (Italy). Dipt. di Matematica]|[Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Trento, Povo (Italy)
2007-12-15
As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J{sup -} common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J{sup -}) constructed on the cosmological horizon. There is exactly one pure quasifree state {lambda} on W(J{sup -}) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore {lambda} induces a preferred physically meaningful quantum state {lambda}{sub M} for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J{sup -}, then the associated self-adjoint generator in the GNS representation of {lambda}{sub M} has positive spectrum (i.e. energy). Moreover {lambda}{sub M} turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, {lambda}{sub M} coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for {lambda}{sub M} in more general spacetimes are presented. (orig.)
Quantum tunneling and field electron emission theories
Liang, Shi-Dong
2013-01-01
Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling. The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the f
Nonequilibrium fermion production in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Pruschke, Jens
2010-06-16
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
A master functional for quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy)
2013-04-15
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional {Gamma} does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=lnZ, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or {Gamma}. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields. (orig.)
Structural aspects of quantum field theory and noncommutative geometry
Grensing, Gerhard
2013-01-01
This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...
Relativistic Quantum Field Theory for Condensed -
MATSUURA, HIROYUKI
We proposed Atomic Schwinger Dyson method (ASD method) in this paper, which was the nonperturbative and finite relativistic quantum field theory, and we treat many electron system and electronic matter. The ASD formalism consists of coupled Dyson equations of electrons and photons. Since, it includes self-energies in a nonperturbative way, higher-order correlations beyond Hartee Fock approximation are taken into account. Some important differences between the ASD formalism for the system of finite electron density and SD formalism of zero electron density are shown. The main difference is due to the existence of condensed photon field, symmetry breaking, and what we call, Coulomb's potential. By paying special attention to the treatment of the condensed photon fields, the coupled Dyson equations of electron and photon are derived based on functional propagator method. It is shown that this treatment of the condensed fields naturally leads to tadpole energy, which cancels the Hartree energy. By using these photon propagators, explicit expression of ASD coupled equations and the energy density of matters are derived for numerical calculations in a subsequent paper. Similarities and differences between ASD and traditional methods such as the mean field theory or the Hartree Fock method are discussed; it is shown that these traditional methods were included in our ASD formalism.
Quantum field theory lectures of Sidney Coleman
Derbes, David; Griffiths, David; Hill, Brian; Sohn, Richard; Ting, Yuan-Sen
2017-01-01
Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the ancient Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.
Quantum gravity as a group field theory: a sketch
Oriti, Daniele
2005-01-01
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
Quantum Field Theories on Categories Fibered in Groupoids
Benini, Marco; Schenkel, Alexander
2017-11-01
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.
Quantum field theory II introductions to quantum gravity, supersymmetry and string theory
Manoukian, Edouard B
2016-01-01
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 in...
Lectures on algebraic quantum field theory and operator algebras
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Berlin Univ. (Germany). Institut fuer Theoretische Physik. E-mail: schroer@cbpf.br
2001-04-01
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)
Quantum field theory in curved spacetime and black hole thermodynamics
Wald, Robert M
1994-01-01
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth. This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum f...
Geometry, topology and quantum field theory (fundamental theories of physics)
Bandyopadhyay, P.
2013-01-01
This monograph deals with the geometrical and topological aspects related to quantum field theory with special reference to the electroweak theory and skyrmions. This book is unique in its emphasis on the topological aspects of a fermion manifested through chiral anomaly which is responsible for the generation of mass. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. These geometrical and topological features help us to consider a massive fermion as a skyrmion and for a composite state we can realise the internal symmetry of hadrons from reflection group. Also, an overview of noncommutative geometry has been presented and it is observed that the manifold M 4 x Z2 has its relevance in the description of a massive fermion as skyrmion when the discrete space is considered as the internal space and the symmetry breaking gives rise to chiral anomaly leading to topological features.
Quantum Probability, Orthogonal Polynomials and Quantum Field Theory
Accardi, Luigi
2017-03-01
The main thesis of the present paper is that: Quantum Probability is not a generalization of classical probability, but it is a deeper level of it. Classical random variables have an intrinsic (microscopic) non-commutative structure that generalize usual quantum theory. The study of this generalization is the core of the non-linear quantization program.
A general field-covariant formulation of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy)
2013-03-15
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general field-covariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W=lnZ behave as scalars. We investigate the relation between composite fields and changes of field variables, and we show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples. (orig.)
Classical fluctuations in quantum field theory
Morikawa, M.
The question as to whether quantum fluctuations can induce the spontaneous breaking of translational invariance (SBTI) in the extreme cosmic expansion that occurs during any type of inflation is considered. Attention is given to the unstable field, thermofield dynamic, and cosmic anisotropic relaxation quantum systems, defining the appropriate order parameters for each and discussing their properties. A mechanism for SBTI is presented which possesses both generality and applicability to various problems; a complex effective potential can, for example, be obtained for a nonconvex potential, so that a random force arises and stochastically agitates order parameters.
Aspects of quantum field theory in curved space-time
Fulling, Stephen A
1989-01-01
The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology
Quantum field theory a tourist guide for mathematicians
Folland, Gerald B
2008-01-01
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theor...
Quantum field theory in generalised Snyder spaces
Energy Technology Data Exchange (ETDEWEB)
Meljanac, S.; Meljanac, D. [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia); Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)
2017-05-10
We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.
Quantum field theory in generalised Snyder spaces
Directory of Open Access Journals (Sweden)
S. Meljanac
2017-05-01
Full Text Available We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.
Quantum field theory in generalised Snyder spaces
Meljanac, S.; Meljanac, D.; Mignemi, S.; Štrajn, R.
2017-05-01
We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Bound states in Galilean-invariant quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Corley, S.R.; Greenberg, O.W. [Center for Theoretical Physics, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States)
1997-02-01
We consider the nonrelativistic quantum mechanics of a model of two spinless fermions interacting via a two-body potential. We introduce quantum fields associated with the two particles as well as the expansion of these fields in asymptotic {open_quotes}in{close_quotes} and {open_quotes}out{close_quotes} fields, including such fields for bound states, in principle. We limit our explicit discussion to a two-body bound state. In this context we discuss the implications of the Galilean invariance of the model and, in particular, show how to include bound states in a strictly Galilean-invariant quantum field theory. {copyright} {ital 1997 American Institute of Physics.}
From PT-symmetric quantum mechanics to conformal field theory
Indian Academy of Sciences (India)
One of the simplest examples of a P T -symmetric quantum system is the scaling Yang–Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in ≤ 2 dimensions, from its original definition in connection with phase transitions in the ...
Quantum Field Theory and Decoherence in the Early Universe
Koksma, J.F.
2011-01-01
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion.
Perturbative quantum gravity in double field theory
Energy Technology Data Exchange (ETDEWEB)
Boels, Rutger H.; Horst, Christoph [II. Institut für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, D- 22761 Hamburg (Germany)
2016-04-19
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
A result in asymmetric Euclidean Ramsey theory
Arman, Andrii; Tsaturian, Sergei
2017-01-01
It is proved that if the points of the three-dimensional Euclidean space are coloured in red and blue, then there exist either two red points unit distance apart, or six collinear blue points with distance one between any two consecutive points.
Vibrations in glasses and Euclidean random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Grigera, T.S.; Martin-Mayor, V.; Parisi, G. [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Rome (Italy); INFN Sezione di Roma - INFM Unita di Roma, Rome (Italy); Verrocchio, P. [Dipartimento di Fisica, Universita di Trento, Povo, Trento (Italy); INFM Unita di Trento, Trento (Italy)
2002-03-11
We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), Euclidean random matrix theory provides a single and fairly simple theoretical framework for their explanation. (author)
Fractional Quantum Field Theory: From Lattice to Continuum
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2014-01-01
Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Nonassociative Snyder ϕ4 quantum field theory
Meljanac, Stjepan; Mignemi, Salvatore; Trampetic, Josip; You, Jiangyang
2017-08-01
In this article, we define and quantize a truncated form of the nonassociative and noncommutative Snyder ϕ4 field theory using the functional method in momentum space. More precisely, the action is approximated by expanding up to the linear order in the Snyder deformation parameter β , producing an effective model on commutative spacetime for the computation of the two-, four- and six-point functions. The two- and four-point functions at one loop have the same structure as at the tree level, with UV divergences faster than in the commutative theory. The same behavior appears in the six-point function, with a logarithmic UV divergence and renders the theory unrenormalizable at β1 order except for the special choice of free parameters s1=-s2. We expect effects from nonassociativity on the correlation functions at β1 order, but these are cancelled due to the average over permutations.
Link fermions in Euclidean lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Brower, R.; Giles, R.; Maturana, G.
1984-02-15
The representation of the Wilson lattice fermion propagator as a sum over classical particle trajectories is discussed. A simple generalization of this path sum leads to an extended set of fermion theories characterized by one (or more) additional parameters. Such theories are nonlocal when written in terms of the usual four-component Dirac field. They are more naturally characterized by a local action functional whose degrees of freedom are those of a set of two-component Fermi fields defined on directed links of the lattice. Such lattice fields correspond to the direct product of a four-vector and Dirac spinor. For a suitable choice of parameters, the extended fermion theory offers a precocious approach to the continuum dispersion relation as the lattice spacing goes to zero and is therefore of interest for numerical studies of QCD.
Concepts in quantum field theory a practitioner's toolkit
Ilisie, Victor
2015-01-01
This book uses less strict yet still formal mathematical language to clarify a variety of concepts in Quantum Field Theory that remain somewhat “fuzzy” in many books designed for undergraduates and fresh graduates. The aim is not to replace formal books on Quantum Field Theory, but rather to offer a helpful complementary tool for beginners in the field. Features include a reader-friendly introduction to tensor calculus and the concept of manifolds; a simple and robust treatment for dimensional regularization; a consistent explanation of the renormalization procedure, step by step and in a transparent manner at all orders, using the QED Lagrangian; and extensive treatment of infrared as well as ultraviolet divergences. The most general (Lorentz invariant) form of Noether's theorem is presented and applied to a few simple yet relevant examples in Quantum Field Theory. These and further interesting topics are addressed in a way that will be accessible for the target readership. Some familiarity with basic no...
Using Wavelet Bases to Separate Scales in Quantum Field Theory
Michlin, Tracie L.
This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.
Quantum Sensors for the Generating Functional of Interacting Quantum Field Theories
Bermudez, A.; Aarts, G.; Müller, M.
2017-10-01
Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in- or out-of-equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories.
Quantum Physics, Fields and Closed Timelike Curves: The D-CTC Condition in Quantum Field Theory
Tolksdorf, Jürgen; Verch, Rainer
2017-07-01
The D-CTC condition has originally been proposed by David Deutsch as a condition on states of a quantum communication network that contains "backward time-steps" in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the D-CTC condition have been discussed extensively in recent literature. In this work, the D-CTC condition is investigated in the framework of quantum field theory in the local, operator-algebraic approach due to Haag and Kastler. It is shown that the D-CTC condition cannot be fulfilled in states that are analytic in the energy, or satisfy the Reeh-Schlieder property, for a certain class of processes and initial conditions. On the other hand, if a quantum field theory admits sufficiently many uncorrelated states across acausally related spacetime regions (as implied by the split property), then the D-CTC condition can always be fulfilled approximately to arbitrary precision. As this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting the D-CTC condition as characteristic for quantum processes in the presence of CTCs could be misleading, and should be regarded with caution. Furthermore, a construction of the quantized massless Klein-Gordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward time-steps, is proposed in this work.
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
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Schenkel, Alexander
2011-10-24
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Lectures on classical and quantum theory of fields
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Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics
2010-07-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)
A General Euclidean Geometric Representation for the Classical Detection Theory
Bayramoglu, Muhammet Fatih
2010-01-01
We propose an Euclidean geometric representation for the classical detection theory. The proposed representation is so generic that can be employed to almost all communication problems. The hypotheses and observations are mapped into R^N in such a way that a posteriori probability of an hypothesis given an observation decreases exponentially with the square of the Euclidean distance between the vectors corresponding to the hypothesis and the observation.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Lectures on classical and quantum theory of fields
Arodz, Henryk
2017-01-01
This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
From field theory to quantum groups
Jancewicz, B
1996-01-01
Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.
Analytic properties of Feynman diagrams in quantum field theory
Todorov, I T
1971-01-01
Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with a
Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions
Martinovic̆, L'ubomír
2017-07-01
A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.
Quantum Field Theory and Decoherence in the Early Universe
Koksma, J. F.
2011-06-01
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired
Mathematical methods of many-body quantum field theory
Lehmann, Detlef
2004-01-01
Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...
Rigorous Quantum Field Theory A Festschrift for Jacques Bros
Monvel, Anne Boutet; Iagolnitzer, Daniel; Moschella, Ugo
2007-01-01
Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. This book arose from an international symposium held in honour of Jacques Bros on the occasion of his 70th birthday, at the Department of Theoretical Physics of the CEA in Saclay, France. The impact of the work of Jacques Bros is evident in several articles in this book. Quantum fields are regarded as genuine mathematical objects, whose various properties and relevant physical interpretations must be studied in a well-defined mathematical framework. The key topics in this volume include analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime. Contributors: D. Bahns, M. Bertola, R. Brunetti, D. Buchholz, A. Connes, F. Corbetta, S. Doplicher, M. Dubois-Violette, M. Dütsch, H. Epstein, C.J. Fewster, K....
Perturbative algebraic quantum field theory an introduction for mathematicians
Rejzner, Kasia
2016-01-01
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions. © 2011 American Institute of Physics.
Aspects of quantum field theory in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Fulling, S.A. (Texas A and M Univ., College Station, TX (USA). Dept. of Mathematics)
1989-01-01
The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the Klein 'paradox', particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalization of the stress tensor. (author).
Quantum field theory the why, what and how
Padmanabhan, Thanu
2016-01-01
This book describes, in clear terms, the Why, What and the How of Quantum Field Theory. The raison d'etre of QFT is explained by starting from the dynamics of a relativistic particle and demonstrating how it leads to the notion of quantum fields. Non-perturbative aspects and the Wilsonian interpretation of field theory are emphasized right from the start. Several interesting topics such as the Schwinger effect, Davies-Unruh effect, Casimir effect and spontaneous symmetry breaking introduce the reader to the elegance and breadth of applicability of field theoretical concepts. Complementing the conceptual aspects, the book also develops all the relevant mathematical techniques in detail, leading e.g., to the computation of anomalous magnetic moment of the electron and the two-loop renormalisation of the self-interacting scalar field. It contains nearly a hundred problems, of varying degrees of difficulty, making it suitable for both self-study and classroom use.
Quantum Field Theory: From Operators to Path Integrals
Huang, Kerson
1998-07-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts
Introduction to a Quantum Theory over a Galois Field
Directory of Open Access Journals (Sweden)
Felix M. Lev
2010-11-01
Full Text Available We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.
On the rate of quantum ergodicity in Euclidean billiards
Bäcker, A; Stifter, P
1998-01-01
For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdière and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we first give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions like bouncing ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a sim...
Quantum field theory in Lorentzian universes from nothing
Friedman, John L.; Higuchi, Atsushi
1995-11-01
We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universes from nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth Lorentzian metric. A time-nonorientable, spacelike hypersurface serves as a generalized Cauchy surface, a surface on which freely specified initial data for wave equations have unique global time evolutions. A simple example is antipodally identified de Sitter space. Classically, such spacetimes are locally indistinguishable from their globally hyperbolic covering spaces. The construction of a quantum field theory is more problematic. Time nonorientability precludes the existence of a global algebra of obsevables, and hence of global states, regarded as positive linear functions on a global algebra. One can, however, define a family of local algebras on an atlas of globally hyperbolic subspacetimes, with overlap conditions on the intersections of neighborhoods. This family locally coincides with the family of algebras on a globally hyperbolic spacetime; and one can ask whether a sensible quantum field theory is obtained if one defines a state as an assignment of a positive linear function to every local algebra. We show, however, that the extension of a generic positive linear function from a single algebra to the collection of all local algebras violates positivity: one cannot find a colleciton of quantum states satisfying the physically appropriate overlap conditions. One can overcome this difficulty by artificially restricting the size of neighborhoods in a way that has no classical counterpart. Neighborhoods in the atlas must be small enough that the union of any pair is time orientable. Correlations between field operators at a pair of points are then defined only if a curve joining the points lies in a single neighborhood. Any state on one neighborhood of an atlas can be extended to a collection of states on the atlas, and the
Relativistic quantum mechanics and introduction to field theory
Energy Technology Data Exchange (ETDEWEB)
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Quantum Yang-Mills field theory
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Relative entropy and proximity of quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Vijay [David Rittenhouse Laboratories, University of Pennsylvania,Philadelphia (United States); CUNY Graduate Center, Initiative for the Theoretical Sciences,New York (United States); Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Heckman, Jonathan J. [Department of Physics, University of North Carolina at Chapel Hill,Chapel Hill (United States); Maloney, Alexander [Department of Physics, McGill University,Montreal (Canada)
2015-05-20
We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions and quantifies the number of measurements required to distinguish between them. In the case of nearby conformal field theories, this reduces to the Zamolodchikov metric on the space of couplings. Our formulation quantifies the information lost under renormalization group flow from the UV to the IR and leads us to a quantification of fine-tuning. This formalism also leads us to a criterion for distinguishability of low energy effective field theories generated by the string theory landscape.
Quantum Hall physics: Hierarchies and conformal field theory techniques
Hansson, T. H.; Hermanns, M.; Simon, S. H.; Viefers, S. F.
2017-04-01
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the 30 years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of non-Abelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
Hack, Thomas-Paul
2015-01-01
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology and a fundamental study of the perturbations in Inflation. The two central sections of the book dealing with these applications are preceded by sections containing a pedagogical introduction to the subject as well as introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation. The target reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but does not need to have a background in QFT on curved spacetimes or the algebraic approach to QFT. In particul...
Applications of Kac-Moody Algebras in Quantum Field Theory.
Cougo Pinto, Marcus Venicius
We apply methods of infinite dimensional algebras to the investigation of two objects from quantum field theory, namely, the vertex operator from bosonic string theory and the set of oscillators from a theory with small violations of the Pauli exclusion principle. For the theory with vertex operators we construct the affine algebra B_sp{l}{(1)} in terms of an underlying Lie-admissible not associative algebra; the construction provides us with a simple mechanism for the onset and elimination of an associativity anomaly involving fermionic variables. We study the Ignat'ev-Kuz'min and Greenberg-Mohapatra algebras, which define the theory with small violations of the Pauli exclusion principle. With the results thus obtained we construct representations of Kac-Moody and Virasoro algebras; those representations in turn are useful in providing some unitary structure for the theory.
Quantum Field Theory in Curved Spacetime
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
The quantum harmonic oscillator on a circle and a deformed quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Rego-Monteiro, M.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: regomont@cbpf.br
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Quantum mean-field theory of collective dynamics and tunneling
Energy Technology Data Exchange (ETDEWEB)
Negele, J.W.
1981-01-01
A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures. (RWR)
Quantum field theory and coalgebraic logic in theoretical computer science.
Basti, Gianfranco; Capolupo, Antonio; Vitiello, Giuseppe
2017-11-01
We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. The q-deformed Hopf Coalgebras and the q-deformed Hopf Algebras constitute two dual categories because characterized by the same functor T, related with the Bogoliubov transform, and by its contravariant application T op , respectively. The q-deformation parameter is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of q identify univocally, and label the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic QFT formulation, as its ability of naturally generating a Fibonacci progression demonstrates. Copyright © 2017 Elsevier Ltd. All rights reserved.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J....... High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance....... Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e-foldings of the inflationary phase....
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Topological quantum field theory: 20 years later
DEFF Research Database (Denmark)
Reshetikhin, Nicolai
2008-01-01
This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory.......This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory....
Nonperturbative studies of quantum field theories on noncommutative spaces
Energy Technology Data Exchange (ETDEWEB)
Volkholz, J.
2007-11-16
This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted
A quantum field theory of the extended electron
Energy Technology Data Exchange (ETDEWEB)
Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica; Recami, Erasmo [Universita Statale di Bergamo, Dalmine, BG (Italy). Facolta di Ingegneria]|[Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada
1993-12-01
In a recent paper, the classical model of Barut and Zanghi (BZ) for the electron spin which interpreted the Zitterbewegung (zbw) motion along helical paths and its quantum version have been investigated by using the language of Clifford algebras. In also doing, a new non-linear Dirac-like equation (NDE) was derived. We want to readdress the whole subject, and complete it, by adopting - for the sake of physical clarity - the ordinary tensorial language. In particular, we re-derive here the NDE for the electron quantum field, show it to be associated with a new conserved probability current, and stress its importance for a quantum field theory of spin 1/2 fermions. Actually, we propose this equation in substitution for the Dirac equation, which comes from the former by averaging over a zbw cycle. We then derive a new equation of motion for the quantum field velocity, which will allow us to regard the electron as an extended object, with a classically intelligible internal structure (thus overcoming some known, long-standing problems). We carefully the solutions of the NDE; with special attention to those implying (at the classical limit) light-like helical motions, since these appear to be the most adequate equations for the electron description, from the kinematical and physical points of view, and do cope with the electron electromagnetic properties (such as Coulomb field and intrinsic magnetic moment). (author). 18 refs.
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Energy Technology Data Exchange (ETDEWEB)
Solomon, A I [Physics and Astronomy Department, Open University, Milton Keynes MK7 6AA (United Kingdom); Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J.-B. Clement, F-93430 Villetaneuse (France); Blasiak, P; Horzela, A [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Division of Theoretical Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Krakow (Poland); Penson, K A, E-mail: a.i.solomon@open.ac.uk, E-mail: gduchamp2@free.fr, E-mail: pawel.blasiak@ifj.edu.pl, E-mail: andrzej.horzela@ifj.edu.pl, E-mail: penson@lptl.jussieu.fr [Lab.de Phys.Theor. de la Matiere Condensee, University of Paris VI (France)
2011-03-01
We show that the combinatorial numbers known as Bell numbers are generic in quantum physics. This is because they arise in the procedure known as Normal ordering of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, inter alia. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the exponential generating function of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.
Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory
Plotnitsky, Arkady
2015-10-01
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
Weyl consistency conditions in non-relativistic quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Pal, Sridip; Grinstein, Benjamín [Department of Physics, University of California,San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)
2016-12-05
Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a C-theorem in higher dimensions.
Dualities Between Semiclassical Strings And Quantum Gauge Field Theories
Ouyang, P
2004-01-01
In this thesis we study several examples of the correspondence between gauge field theories and string theories. A recurrent theme of these studies is that distinctively quantum mechanical behavior on the gauge theory side of the correspondence can have a classical or semiclassical description in terms of string calculations, as one might expect from general considerations of open/closed duality. We begin in Chapter 1 by reviewing the simplest duality, which relates Type IIB supergravity in AdS5 × S5 to N = 4 SU(N) gauge theory at large N. Working with this background spacetirne, we turn to a study of D-brane probes with large quantum numbers in Chapter 2. We employ semiclassical methods to compute the excitation spectrum of these D-branes, including corrections of order 1/N, which are related to loop effects in the dual field theory. In Chapter 3 we discuss the gauge/gravity duals with N = 1 supersymmetry which arise from placing D- branes at a conifold singularity. The inclusion of fraction...
Local Properties of Measures in Quantum Field Theory and Cosmology
Velhinho, José M.
2015-01-01
We show that measure theoretical results concerning the Ashtekar-Lewandowski measure in the space of generalized connections have direct analogues in the context of the Bohr compactification of the line and associated Haar measure. We present also a characterization of the support of the measure associated with the canonical quantization of the free massive scalar field, following closely well known analogous results concerning the Euclidean path integral measure.
Deformations of quantum field theories on spacetimes with Killing vector fields
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Dappiaggi, Claudio [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lechner, Gandalf [Wien Univ. (Austria). Fakultaet fuer Physik; Morfa-Morales, Eric [Erwin Schroedinger Institut fuer Mathematische Physik, Wien (Austria)
2010-06-15
The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincare transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied. (orig.)
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Novel Approaches To Numerical Solutions Of Quantum Field Theories
Petrov, D
2005-01-01
Two new approaches to numerically solving Quantum Field Theories are presented. The Source Galerkin technique is a direct approach to determining the generating functional of a theory by solving the Schwinger-Dyson equations. The properties of the Source Galerkin technique are tested by using it to determine the phase structure of the Ultralocal &phis;4 theory. A framework for applying this approach to solving O( N) Nonlinear Sigma model is constructed. The Sinc Function approximation is a highly efficient method of numerically evaluating Feynman diagrams. In the present dissertation the Sinc Function approximation is applied to fermionic fields. The Sinc expanded versions of fermion and photon propagators are derived. The accuracy of this approximation is tested by a direct comparison of the Sinc expanded propagators with exact propagators and by performing several sample calculations of one loop QED diagrams. An analysis of computational properties of the Sinc Function approach is presented.
Reducibility and Gribov Problem in Topological Quantum Field Theory
Zucchini, Roberto
In spite of its simplicity and beauty, the Mathai-Quillen formulation of cohomological topological quantum field theory with gauge symmetry suffers two basic problems: i) the existence of reducible field configurations on which the action of the gauge group is not free and ii) the Gribov ambiguity associated with gauge fixing, i. e. the lack of global definition on the space of gauge orbits of gauge fixed functional integrals. In this paper, we show that such problems are in fact related and we propose a general completely geometrical recipe for their treatment. The space of field configurations is augmented in such a way to render the action of the gauge group free and localization is suitably modified. In this way, the standard Mathai-Quillen formalism can be rigorously applied. The resulting topological action contains the ordinary action as a subsector and can be shown to yield a local quantum field theory, which is argued to be renormalizable as well. The salient feature of our method is that the Gribov problem is inherent in localization, and thus can be dealt within a completely equivariant setting, whereas gauge fixing is free of Gribov ambiguities. For the stratum of irreducible gauge orbits, the case of main interest in applications, the Gribov problem is solvable. Conversely, for the strata of reducible gauge orbits, the Gribov problem cannot be solved in general and the obstruction may be described in the language of sheaf theory. The formalism is applied to the Donaldson-Witten model.
Quantum theory of strong-field frustrated tunneling
Popruzhenko, S. V.
2018-01-01
We show how the strong-field approximation, widely used for description of multiphoton and tunneling ionization, can be extended to analyse the excitation of bound states in intense low-frequency laser pulses. The proposed theory is based on the formalism of quantum trajectories and fills the gap between the numerical solution of the time-dependent Schrödinger equation and classical simulations. In particular, it allows identifying non-adiabatic and interference effects in strong-field excitation of Rydberg states.
Working directly with probabilities in quantum field theory
Dickinson, R.; Forshaw, J.; Millington, P.
2017-08-01
We present a novel approach to computing transition probabilities in quantum field theory, which allows them to be written directly in terms of expectation values of nested commutators and anti-commutators of field operators, rather than squared matrix elements. We show that this leads to a diagrammatic expansion in which the retarded propagator plays a dominant role. As a result, one is able to see clearly how faster-than-light signalling is prevented between sources and detectors. Finally, we comment on potential implications of this approach for dealing with infra-red divergences.
A course on quantum field theory and local observables
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Frankfurt Univ., Berlin (Germany). Inst. fuer Theoretische Physik
1997-03-01
A monograph on Quantum Field Theory and Local Observables is presented, aiming to unify two presently largely disconnected branches of QFT, as follows: the standard (canonical, functional) approach which is mainly perturbative in the sense of an infinitesimal `deformation` of free fields; nonperturbative constructions of low-dimensional models as the form factor-bootstrap approach (which for the time being is limited to factorable models in d=1+1 spacetime dimensions) and the non-Lagrangian constructions of conformal chiral QFT`s
Principles of physics from quantum field theory to classical mechanics
Jun, Ni
2014-01-01
This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced gradua...
Master functional and proper formalism for quantum gauge field theory
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy)
2013-03-15
We develop a general field-covariant approach to quantum gauge theories. Extending the usual set of integrated fields and external sources to ''proper'' fields and sources, which include partners of the composite fields, we define the master functional {Omega}, which collects one-particle irreducible diagrams and upgrades the usual {Gamma}-functional in several respects. The functional {Omega} is determined from its classical limit applying the usual diagrammatic rules to the proper fields. Moreover, it behaves as a scalar under the most general perturbative field redefinitions, which can be expressed as linear transformations of the proper fields. We extend the Batalin-Vilkovisky formalism and the master equation. The master functional satisfies the extended master equation and behaves as a scalar under canonical transformations. The most general perturbative field redefinitions and changes of gauge-fixing can be encoded in proper canonical transformations, which are linear and do not mix integrated fields and external sources. Therefore, they can be applied as true changes of variables in the functional integral, instead of mere replacements of integrands. This property overcomes a major difficulty of the functional {Gamma}. Finally, the new approach allows us to prove the renormalizability of gauge theories in a general field-covariant setting. We generalize known cohomological theorems to the master functional and show that when there are no gauge anomalies all divergences can be subtracted by means of parameter redefinitions and proper canonical transformations. (orig.)
Functional integrals and inequivalent representations in Quantum Field Theory
Blasone, M.; Jizba, P.; Smaldone, L.
2017-08-01
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle due to the existence of unitarily inequivalent representations of canonical commutation relations. When one works with functional integrals, it is not immediately clear how this algebraic feature manifests itself in the formalism. Here we attack this issue by considering the canonical transformations in the context of coherent-state functional integrals. Specifically, in the case of linear canonical transformations, we derive the general functional-integral representations for both transition amplitude and partition function phrased in terms of new canonical variables. By means of this, we show how in the infinite-volume limit the canonical transformations induce a transition from one representation of canonical commutation relations to another one and under what conditions the representations are unitarily inequivalent. We also consider the partition function and derive the energy gap between statistical systems described in two different representations which, among others, allows to establish a connection with continuous phase transitions. We illustrate the inner workings of the outlined mechanism by discussing two prototypical systems: the van Hove model and the Bogoliubov model of weakly interacting Bose gas.
Towards a quantum field theory of primitive string fields
Energy Technology Data Exchange (ETDEWEB)
Ruehl, W., E-mail: wue_ruehl@t-online.de [Technical University of Kaiserslautern, Department of Physics (Germany)
2012-10-15
We denote generating functions of massless even higher-spin fields 'primitive string fields' (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS{sub d+1} are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 {<=} N {<=}{infinity} play for us the role of 'standard models', for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = {infinity}. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s {>=} 4, they are distinguished by their anomalous dimensions (in CFT{sub 3}) or by theirmass (in AdS{sub 4}). We sum over these multiplets and the spins to obtain 'string type fields', one for each such monomial.
Towards a quantum field theory of primitive string fields
Rühl, W.
2012-10-01
We denote generating functions of massless even higher-spin fields "primitive string fields" (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS d+1 are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O( N) invariant sectors of the O( N) vector models for 1 ≤ N ≤∞ play for us the role of "standard models", for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = ∞. A formula for the masses squared that break gauge symmetry for these O( N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s ≥ 4, they are distinguished by their anomalous dimensions (in CFT 3) or by theirmass (in AdS 4). We sum over these multiplets and the spins to obtain "string type fields", one for each such monomial.
Simulating thimble regularization of lattice quantum field theories
Di Renzo, Francesco
2016-01-01
Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow lines. The latter are the steepest ascent paths attached to critical points, i.e. the basic building blocks of thimbles. The measure to sample is thus dictated by the contribution of complete flow lines to the partition function. The algorithm is based on a heat bath sampling of the gaussian approximation of the thimble: this defines the proposals for a Metropolis-like accept/reject step. The effectiveness of the algorithm has been tested on a few models, e.g. the chiral random matrix model. We also discuss thimble regularization of gauge theories, and in particular the successfull application to 0+1 dimensional QCD and the status and prospects for Yang-Mills theories.
Precision decay rate calculations in quantum field theory
Andreassen, Anders; Farhi, David; Frost, William; Schwartz, Matthew D.
2017-04-01
Tunneling in quantum field theory is worth understanding properly, not least because it controls the long-term fate of our Universe. There are, however, a number of features of tunneling rate calculations which lack a desirable transparency, such as the necessity of analytic continuation, the appropriateness of using an effective instead of classical potential, and the sensitivity to short-distance physics. This paper attempts to review in pedagogical detail the physical origin of tunneling and its connection to the path integral. Both the traditional potential-deformation method and a recent, more direct, propagator-based method are discussed. Some new insights from using approximate semiclassical solutions are presented. In addition, we explore the sensitivity of the lifetime of our Universe to short-distance physics, such as quantum gravity, emphasizing a number of important subtleties.
Topics in string theory and quantum gravity
Alvarez-Gaume, Luis
1992-01-01
These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) ...
A non-renormalization theorem in gapped quantum field theory
Shacham, Tomer
2013-05-01
We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that at zero momentum, the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does not receive quantum corrections.
Equivariant topological quantum field theory and symmetry protected topological phases
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)
2017-03-01
Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.
Periodic Euclidean solutions of SU(2)-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Frost, K.L.; Yaffe, L.G. [University of Washington, Department of Physics, Seattle, Washington 98105-1560 (United States)
1999-03-01
We examine periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. Classical perturbation theory is used to construct periodic time-dependent solutions in the neighborhood of the static sphaleron. The behavior of the action, as a function of period, changes character depending on the value of the Higgs boson mass. The required pattern of bifurcations of solutions as a function of the Higgs boson mass is examined, and implications for the temperature dependence of the baryon number violation rate in the standard model are discussed. {copyright} {ital 1999} {ital The American Physical Society}
Real time quantum field theory on a computer: The Hartree ensemble approximation
Sallé, M.
2002-01-01
The main motivation for this thesis is the physics of the very early universe and of heavy ion collisions. These two fields are described using quantum field theory. In order to do calculations in (quantum) field theory one often makes use of perturbation theory and/or the imaginary time formalism.
Euclidean Epstein-Glaser renormalization
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Keller, Kai J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2009-03-15
In the framework of perturbative Algebraic Quantum Field Theory (pAQFT) I give a general construction of so-called 'Euclidean time-ordered products', i.e. algebraic versions of the Schwinger functions, for scalar quantum eld theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space (MQFT). An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction-) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of EQFT have a unique singularity structure, i.e. they are unique up to a smooth part. Second, one needs to (re-)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable. (orig.)
Infinitely many inequivalent field theories from one Lagrangian
100__; Mavromatos, Nick E.; Sarkar, Sarben
2014-01-01
Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field $\\phi$. In Euclidean space the Lagrangian of such a theory, $L=\\frac{1}{2}(\
Group field theory for quantum gravity minimally coupled to a scalar field
Li, Yang; Oriti, Daniele; Zhang, Mingyi
2017-10-01
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman expansion. We also analyze a number of variations of the same model, the corresponding discrete gravity path integrals, its generalization to the coupling of multiple scalar fields and discuss its possible applications to the extraction of effective cosmological dynamics from the full quantum gravity formalism, in the context of group field theory condensate cosmology.
Mean-field theory of quantum Brownian motion
Allahverdyan, A.; Balian, R.
2001-01-01
We investigate a mean-field approach to a quantum Brownian particle interacting with a quantum thermal bath at temperature T, and subjected to a non-linear potential. An exact, partially classical description of quantum Brownian motion is proposed, which uses negative probabilities in its
Quantum Field Theory as a Faithful Image of Nature
Öttinger, Hans Christian
2015-01-01
"All men by nature desire to know," states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not top on the priority list, not only for physicists and philosophers. The goal of the present book is to contribute to this knowledge by going beyond the usual presentations of quantum field theory in physics textbooks, both in mathematical approach and by critical reflections inspired by epistemology, that is, by the branch of philosophy also referred to as the theory of knowledge. Hopefully, the present book motivates physicists to appreciate philosophical ideas. Epistemology and the philosophy of the evolution of science often seem to lag behind science and to describe the developments a posteriori. As philosophy here has a profound influence on the actual shaping of an image of fundamental particles and their interactions, our development should stimulate the curiosity and...
The ontology of quantum field theory: Structural realism vindicated?
Glick, David
2016-10-01
In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. Copyright © 2016 Elsevier Ltd. All rights reserved.
DFR Perturbative Quantum Field Theory on Quantum Space Time, and Wick Reduction
Piacitelli, Gherardo
We discuss the perturbative approach à la Dyson to a quantum field theory with nonlocal self-interaction :φ⋆···⋆φ, according to Doplicher, Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction of nonlocally time-ordered products of Wick monomials can be performed as usual, and we discuss a very simple Dyson diagram.
(Studies in quantum field theory: Progress report, April 1, 1991--March 31, 1992)
Energy Technology Data Exchange (ETDEWEB)
Bender, C M
1992-01-01
Professors Bender, Bernard, and Shrauner, Assistant Professors Ogilvie and Goltermann, Research Assistant Professors Visser and Petcher, and Research Associate Rivas are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: lattice gauge calculations of masses and weak matrix elements; strong-coupling approximation; low-energy effective field theories; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; the nature of perturbation theory in large order; quark condensation in QCD; chiral fermion theories on the lattice; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD; studies of the early universe and inflation; quantum gravity. This work is described in detail in the body of this proposal.
Peskin, Michael E.
2011-04-01
Anthony Zee is not only a leading theoretical physicist but also an author of popular books on both physics and non-physics topics. I recommend especially `Swallowing Clouds', on Chinese cooking and its folklore. Thus, it is not surprising that his textbook has a unique flavor. Derivations end, not with `QED' but with exclamation points. At the end of one argument, we read `Vive Cauchy!', in another `the theorem practically exudes generality'. This is quantum field theory taught at the knee of an eccentric uncle; one who loves the grandeur of his subject, has a keen eye for a slick argument, and is eager to share his repertoire of anecdotes about Feynman, Fermi, and all of his heroes. A one-page section entitled `Electric Charge' illustrates the depth and tone of the book. In the previous section, Zee has computed the Feynman diagram responsible for vacuum polarization, in which a photon converts briefly to a virtual electron-positron pair. In the first paragraph, he evaluates this expression, giving a concrete formula for the momentum-dependence of the electric charge, an important effect of quantum field theory. Next, he dismisses other possible diagrams that could affect the value of the electric charge. Most authors would give an explicit argument that these diagrams cancel, but for Zee it is more important to make the point that this result is expected and, from the right point of view, obvious. Finally, he discusses the implications for the relative size of the charges of the electron and the proton. If the magnitudes of charges are affected by interactions, and the proton has strong interactions but the electron does not, can it make sense that the charges of the proton and the electron are exactly equal and opposite? The answer is yes, and also that this was the real point of the whole derivation. The book takes on the full range of topics covered in typical graduate course in quantum field theory, and many additional topics: magnetic monopoles, solitons
Perturbative unitarity of Lee-Wick quantum field theory
Anselmi, Damiano; Piva, Marco
2017-08-01
We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and the values of a loop integral in the various regions are related to one another by a nonanalytic procedure. We show that the one-loop diagrams satisfy the expected, unitary cutting equations in each region: only the physical d.o.f. propagate through the cuts. The goal can be achieved by working in suitable subsets of each region and proving that the cutting equations can be analytically continued as a whole. We make explicit calculations in the cases of the bubble and triangle diagrams and address the generality of our approach. We also show that the same higher-derivative models violate unitarity if they are formulated directly in Minkowski spacetime.
Quantum Monte Carlo calculations with chiral effective field theory interactions
Energy Technology Data Exchange (ETDEWEB)
Tews, Ingo
2015-10-12
The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By
Spectral and scattering theory for translation invariant models in quantum field theory
DEFF Research Database (Denmark)
Rasmussen, Morten Grud
This thesis is concerned with a large class of massive translation invariant models in quantum field theory, including the Nelson model and the Fröhlich polaron. The models in the class describe a matter particle, e.g. a nucleon or an electron, linearly coupled to a second quantised massive scalar...
Quantum revivals in conformal field theories in higher dimensions
Cardy, John
2016-10-01
We investigate the behavior of the return amplitude { F }(t)=| | following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension d-1 and linear size O(L), from a state | {{\\Psi }}(0)> of extensive energy with short-range correlations. After an initial gaussian decay { F }(t) reaches a plateau value related to the density of available states at the initial energy. However for d=3,4 this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least O({σ }1/(d-1)L), where σ \\gg 1 is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times t˜ {{integer}}× L. In particular, on a sphere {S}d-1 of circumference 2π L, there is an action of the modular group on { F }(t) implying structure near all rational values of t/L, similar to what happens for rational CFTs in d=2.
On some aspects of the definition of scattering states in quantum field theory
Toth, Gabor Zsolt
2009-01-01
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states b...
Quantum field theory of polyelectrolyte-counterion condensation
Dewey, T. G.
1988-10-01
A simple quantum theory of polyelectrolyte-counterion interactions is presented. A model Hamiltonian is employed which describes both the polyelectrolyte and the counterion as free, spinless fermions. This Hamiltonian is transformed into a form which is isomorphous with traditional Hamiltonians used to describe phase transitions. The difference between this theory and early theories of superconductivity is that the counterion-counterion interaction energies will be quite large and will persist at high temperatures. The counterion condensate is a collective mode resulting from polyelectrolyte-mediated polarizations. Colligative properties for this model are compared with the Poisson-Boltzmann theory and to Manning's condensation theory.
Quantum field theory with infinitive component local fields as an alternative to the string theories
Energy Technology Data Exchange (ETDEWEB)
Krasnikov, N.V.
1987-09-10
We show that the introduction of the infinite component local fields with higher-order derivatives in the interaction makes the theory completely ultraviolet finite. For the ..gamma../sub 5/-anomalous theories the introduction of the infinite component field makes the theory renormalizable or even superrenormalizable.
A new class of group field theories for 1st order discrete quantum gravity
Oriti, D.; Tlas, T.
2008-01-01
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman
Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis
McGown, Kevin J.
2011-01-01
Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant $\\Delta=7^2,9^2,13^2,19^2,31^2,37^2,43^2,61^2,67^2,103^2,109^2,127^2,157^2$. A large part of the proof is in establishing the following more general result: Let $K$ be a Galois number field of odd prime degree $\\ell$ and conductor $f$. Assume the GRH for $\\zeta_K(s)$. If $38(\\ell-1)^2(\\log f)^6\\log\\log f
Topics in quantum field theory; Topicos em teoria quantica dos campos
Energy Technology Data Exchange (ETDEWEB)
Svaiter, N.F
2006-11-15
This paper presents some important aspects on quantum field theory, covering the following aspects: the triumph and limitations of the quantum field theory; the field theory in curved spaces - Hawking and Unruh-Davies effects; the problem of divergent theory of the zero-point; the problem of the spinning detector and the Trocheries-Takeno vacuum; the field theory at finite temperature - symmetry breaking and phase transition; the problem of the summability of the perturbative series and the perturbative expansion for the strong coupling; quantized fields in presence of classical macroscopic structures; the Parisi-Wu stochastic quantization method.
Topics in brane world and quantum field theory
Corradini, Olindo
In the first part of the thesis we study various issues in the Brane World scenario with particular emphasis on gravity and the cosmological constant problem. First, we study localization of gravity on smooth domain-wall solutions of gravity coupled to a scalar field. In this context we discuss how the aforementioned localization is affected by including higher curvature terms in the theory, pointing out among other things that, general combinations of such terms lead to delocalization of gravity with the only exception of the Gauss-Bonnet combination (and its higher dimensional counterparts). We then find a solitonic 3-brane solution in 6D bulk in the Einstein-Hilbert-Gauss-Bonnet theory of gravity. Near to the brane the metric is that for a product of the 4D flat Minkowski space with a 2D wedge whose deficit angle is proportional to the brane tension. Consistency tests imposed on such backgrounds appear to require the localized matter on the brane to be conformal. We then move onto infinite volume extra dimension Brane World scenarios where we study gravity in a codimension-2 model, generalizing the work of Dvali, Gabadadze and Porrati to tensionful branes. We point out that, in the presence of the bulk Gauss-Bonnet combination, the Einstein-Hilbert term is induced on the brane already at the classical level. Consistency tests are presented here as well. To conclude we discuss, using String Theory, an interesting class of large-N gauge theories which have vanishing energy density even though these theories are non-covariant and non-supersymmetric. In the second part of the thesis we study a formulation of Quantum Mechanical Path Integrals in curved space. Such Path Integrals present superficial divergences which need to be regulated. We perform a three-loop calculation in mode regularization as a nontrivial check of the non-covariant counterterms required by such scheme. We discover that dimensional regularization can be successfully adopted to evaluate the
Entanglement in Lifshitz-type quantum field theories
Mohammadi Mozaffar, M. Reza; Mollabashi, Ali
2017-07-01
We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.
Diffeomorphism Group Representations in Relativistic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Fiorentini, D.; Sorella, S.P. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Pereira, A.D. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); UFF - Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-08-15
In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hepth]), Pereira et al. (arXiv:1605.09747 [hep-th]), the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement. (orig.)
Fuzzy Euclidean wormholes in de Sitter space
Chen, Pisin; Yeom, Dong-han
2016-01-01
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a quantum big bounce from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some lights to the resolution of the singularity and tensions between various kinds of quantum gravity theories.
From PT -symmetric quantum mechanics to conformal field theory
Indian Academy of Sciences (India)
Deep in the ultraviolet regime the properties of the scaling Yang–Lee model are governed by the conformal field theory M2,5 [12,13] which has a negative central charge and a single relevant spin-zero field φ, with negative conformal dimensions. The off-critical integrable version of the model corresponds to the perturbation ...
Bischoff, Marcel; Longo, Roberto; Rehren, Karl-Henning
2015-01-01
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
Universal resistance quantum in multichannel transport and dissipative field theory
Dutt, Prasenjit; Schmidt, Thomas; Le Hur, Karyn
2012-02-01
The Landauer formula for coherent DC transport lies at the heart of nanoelectronics and embodies a startling prediction: the quantization of the conductance in one-dimensional metallic wires for ballistic transport, in steps of Rq-1=e^2/h for each channel. Scattering proccesses undergone by the electrons cause a deviation from this result. The resistance then depends on the transparency of the channel and assumes a nonuniversal value. Recently, the unit of resistance Rq has been shown to be a universal feature for AC transport through a single-channel quantum RC circuit with a large cavity. This result can be understood by mapping the system to the one-channel Kondo model and the emergent low-energy Fermi-liquid theory. In a different context Rq arises in a certain nonequilibrium setting for the multichannel quantum RC circuit. In this work, we study AC transport in the many-channel quantum RC circuit. Under certain well-defined conditions the charge relaxation resistance remains universal and equals Rq. We study the emergence of this universal resistance in the multi-channel limit by using the mapping with a dissipative particle on a ring and making an analogy with the Kondo model.
Obstruction of black hole singularity by quantum field theory effects
Energy Technology Data Exchange (ETDEWEB)
Abedi, Jahed; Arfaei, Hessamaddin [Department of Physics, Sharif University of Technology,P.O. Box 11155-9161, Tehran, Irany (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2016-03-21
We consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of (c{sub A}(M/(M{sub p}))){sup 1/3}l{sub p}. After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effects the coupling of field to gravity as trace anomaly of quantum fluctuations the formation of the singularity through collapse is obstructed. An important consequence of our work is existence of an extremal solution with zero temperature and a mass which is lower bound for the Schwazschild solution. This solution is also the asymptotic final stable state after Hawking radiation.
On some aspects of the definition of scattering states in quantum field theory
Tóth, Gábor
2012-04-01
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the applications and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.
Quantum electronics basic theory
Fain, V M; Sanders, J H
1969-01-01
Quantum Electronics, Volume 1: Basic Theory is a condensed and generalized description of the many research and rapid progress done on the subject. It is translated from the Russian language. The volume describes the basic theory of quantum electronics, and shows how the concepts and equations followed in quantum electronics arise from the basic principles of theoretical physics. The book then briefly discusses the interaction of an electromagnetic field with matter. The text also covers the quantum theory of relaxation process when a quantum system approaches an equilibrium state, and explai
Fuzzy Euclidean wormholes in de Sitter space
Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han
2017-07-01
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.
Conformal Generally Covariant Quantum Field Theory: The Scalar Field and its Wick Products
Pinamonti, Nicola
2009-06-01
In this paper we generalize the construction of generally covariant quantum theories given in [BFV03] to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought of as natural transformations in the sense of category theory. We show that the Wick monomials without derivatives (Wick powers) can be interpreted as fields in this generalized sense, provided a non-trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale μ appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields.
Flat connection, conformal field theory and quantum group
Energy Technology Data Exchange (ETDEWEB)
Kato, Mitsuhiro.
1989-07-01
General framework of linear first order differential equation for four-point conformal block is studied by using flat connection. Integrability and SL{sub 2} invariance restrict possible form of flat connection. Under a special ansatz classical Yang-Baxter equation appears as an integrability condition and the WZW model turns to be unique conformal field theory in that case. Monodromy property of conformal block can be easily determined by the flat connection. 11 refs.
Rigorous Limits on the Interaction Strength in Quantum Field Theory
Caracciolo, Francesco
2009-01-01
We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1
Locally covariant quantum field theory and the spin-statistics connection
Fewster, Christopher J
2016-01-01
The framework of locally covariant quantum field theory, an axiomatic approach to quantum field theory in curved spacetime, is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. This part of the text is based on arXiv:1503.05797 and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.
Topological defects in quantum field theory with matrix product states
Gillman, Edward; Rajantie, Arttu
2017-11-01
Topological defects (kinks) in a relativistic ϕ4 scalar field theory in D =(1 +1 ) are studied using the matrix product state tensor network. The one kink state is approximated as a matrix product state and the kink mass is calculated. The approach used is quite general and can be applied to a variety of theories and tensor networks. Additionally, the contribution of kink-antikink excitations to the ground state is examined and a general method to estimate the scalar mass from equal time ground state observables is provided. The scalar and kink mass are compared at strong coupling and behave as expected from universality arguments. This suggests that the matrix product state can adequately capture the physics of defect-antidefect excitations and thus provides a promising technique to study challenging nonequilibrium physics such as the Kibble-Zurek mechanism of defect formation.
Quantum field theory and the antipodal identification of space time
Energy Technology Data Exchange (ETDEWEB)
Domenech, G.; Levinas, M.L. (IAFE-CONICET, C.C. 67, Suc. 28, 1428, Buenos Aires (AR)); Sanchez, N. (UA 336 CNRS-DEMIRM, Observatoire de Paris, Section de Meudon, 92195 Meudon Principal Cedex (FR))
1988-01-01
The authors investigate the elliptic interpretation of space-time (identification of antipodal points or vents) in anti-deSitter and in Rindler manifolds and its consequences for QFT. They compare and give a complete description of antipodal identification in space-times with and without event horizons. Antipodal identification relates the field theories on deSitter and on anti-deSitter spaces. In the elliptic Rindler manifold, imaginary time is periodic with period {beta}/2 but the Green functions (for both identifications with and without Conical singularity) have period {beta}. Additional new properties for the Green functions are obtained and the new terms added to the stress tensor computed.
A Non-Renormalization Theorem in Gapped Quantum Field Theory
Shacham, Tomer
2013-01-01
We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does no...
ICTP Summer Course on Low-Dimensional Quantum Field Theories for Condensed Matter Physicists
Morandi, G; Lu, Y
1995-01-01
This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks.
Numerical Calculations Of Quantum Field Theories On The Continuum
Emirdag, P
2002-01-01
Source Galerkin technique is an alternative numerical method developed by Garcìa, Guralnik, and Lawson at Brown. It is not based on any statistical methods and has controllable errors. It also has the advantage that it can be used in a continuum formulation. This new method promises an increase in accuracy and speed of calculations. In this method, we treat field theory with the presence of external sources. The functional relations become a set of coupled differential equations for the generating functional Z. Source Galerkin is used to solve these equations for the Green's functions of the theory. According to this technique, the set of the residuals and the test functions are required to be orthogonal with respect to some inner product. The test functions that we are using are polynomials that consists of source terms and preserve the group symmetry of the problem. Symmetries of translation and reflection invariance are used in constructing the solution. A good choice of the test functions and t...
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of
Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Anomalies in quantum field theory and differential geometry
Energy Technology Data Exchange (ETDEWEB)
Manes, J.L.
1986-04-01
Anomalies in field theory appeared first in perturbative computations involving Feynman diagrams. It is only recently that differential geometric techniques have been used to obtain the form of gauge and gravitational anomalies in a direct and simple way. This is possible because of the topological nature of the anomaly. In the first chapter of this thesis the gauged Wess-Zumino action is constructed by differential geometry methods. After reviewing the relevant techniques, an expression for the action valid in any (even) number of space-time dimensions is obtained. This expression is compared with Witten's result in four dimensions. The link between topology and the anomaly is provided by the appropriate index theorem. The index density is a supersymmetric invariant polynomial from which the anomaly and other related objects can be obtained through the use of the ''descent equations.'' A new proof of the Atiyah-Singer index theorem for the Dirac operator is presented. This proof is based on the use of a WKB approximation to evaluate the supertrace of the kernel for a supersymmetric hamiltonian. The necessary WKB techniques are developed and mechanical systems with bosonic and fermionic degrees of freedom are discussed.
Energy Technology Data Exchange (ETDEWEB)
Bauer, W.
2007-03-15
The goal of this diploma thesis is to present an overview of how to reduce the problem of topology change of general spacetimes to the investigation of elementary cobordisms. In the following we investigate the possibility to construct quantum fields on elementary cobordisms, in particular we discuss the trousers topology. Trying to avoid the problems occuring at spacetimes with instant topology change we use a model for simulating topology change. We construct the algebra of observables for a free scalar field with the algebraic approach to quantum field theory. Therefore we determine a fundamental solution of the eld equation. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Corrigan, E., E-mail: edward.corrigan@durham.ac.u [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom); Zambon, C., E-mail: cristina.zambon@durham.ac.u [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)
2011-07-21
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite-dimensional representation of the relevant Borel subalgebra of the quantum group underpinning the integrable quantum field theory and a particular infinite-dimensional representation expressed in terms of sets of generalised 'quantum' annihilation and creation operators. The principal examples analysed are based on the a{sub 2}{sup (2)} and a{sub n}{sup (1)} affine Toda models but examples of similar infinite-dimensional representations for quantum Borel algebras for all other affine Toda theories are also provided.
Remarks on quantum field theory on de Sitter and anti-de Sitter ...
Indian Academy of Sciences (India)
2012-06-14
Jun 14, 2012 ... The literature devoted to quantum field theory (QFT) on the de Sitter and anti-de Sitter space-times is enormous. This short review is limited to work done in recent years with the authors quoted in the abstract. The most significant results described here are the two explicit Källén–Lehmann representations ...
Problems of perturbation series in non-equilibrium quantum field theories
Altherr, Tanguy
1994-01-01
In the standard framework of non-equilibrium quantum field theories, the pinch singularities associated to multiple products of \\delta-functions do not cancel in a perturbative expansion unless the particle distributions are those for a system in thermal and chemical equilibrium.
Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Delfino, G. [International School of Advanced Studies (SISSA), Trieste (Italy)]|[INFN sezione di Trieste (Italy); Niccoli, G. [Univ. de Cergy-Pontoise (France). LPTM
2007-12-15
For the simplest quantum field theory originating from a non-trivial fixed point of the renormalization group, the Lee-Yang model, we show that the operator space determined by the particle dynamics in the massive phase and that prescribed by conformal symmetry at criticality coincide. (orig.)
Relativistic Violation Invariance, Multiverses and Quantum Field Theory
Gamboa, J.; Loewe, M.; Mendez, F.
2003-01-01
The possibility of interaction among multiverses is studied assuming that in the first instants of the big-bang, many disjoint regions were created producing many independent universes (multiverses). Many of these mini-universes were unstable and they decayed, but other remained as topological remnant (like domain walls or baby universes) or possibly as mini-black-holes. In this paper, we study the quantum statistical mechanics of multiverses assuming that in the first instants of the big-ban...
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity
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Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Freie Univ., Berlin (Germany). Institut fuer Theoretische Physik]. E-mail: schroer@cbpf.br
2007-07-01
We show that there are significant conceptual differences between QM and QFT which make it difficult to view QFT as just a relativistic extension of the principles of QM. The root of this is a fundamental distinction between Born-localization in QM (which in the relativistic context changes its name to Newton-Wigner localization) and modular localization which is the localization underlying QFT, after one liberates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects. Taking these significant differences serious has not only repercussions for the philosophy of science, but also leads to a new structural properties as a consequence of vacuum polarization: the area law for localization entropy near the the causal localization horizon and a more realistic cutoff independent setting for the cosmological vacuum energy density which is compatible with local covariance. (author)
Quantum field theory in spaces with closed time-like curves
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Boulware, D.G.
1992-12-31
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Boundary terms in quantum field theory and the spin structure of QCD
Directory of Open Access Journals (Sweden)
Peter Lowdon
2014-12-01
Full Text Available Determining how boundary terms behave in a quantum field theory (QFT is crucial for understanding the dynamics of the theory. Nevertheless, boundary terms are often neglected using classical-type arguments which are no longer justified in the full quantum theory. In this paper we address this problem by establishing a necessary and sufficient condition for arbitrary spatial boundary terms to vanish in a general QFT. As an application of this condition we examine the issue of whether the angular momentum operator in Quantum Chromodynamics (QCD has a physically meaningful quark–gluon decomposition. Using this condition it appears as though this is not the case, and that it is in fact the non-perturbative QCD structure which prevents the possibility of such a decomposition.
Quantum field theory of photon-Dirac fermion interacting system in graphene monolayer
Nguyen, Bich Ha; Hieu Nguyen, Van
2016-06-01
The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields.
On the construction of quantum field theories with factorizing S-matrices
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Lechner, G.
2006-05-24
The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. Employing the algebraic framework of quantum field theory, it is shown under which conditions an algebra of observables localized in a wedge-shaped region of spacetime can be used to construct model theories. A crucial input in this context is the modular nuclearity condition for wedge algebras, which implies the existence of local observables. As an application of the new method, a rigorous construction of a large family of models with factorizing S-matrices is obtained. In an inverse scattering approach, a given factorizing scattering operator is used to define certain semi-localized Wightman fields associated to it. With the help of these fields, a wedge algebra can be defined, which determines the local observable content of a well-defined quantum field theory. In this approach, the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge-local observables. These conditions are shown to hold for a large class of underlying S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples. The so constructed models are investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the underlying S-matrices, and a proof of asymptotic completeness for these models is given. (orig.)
Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.
1980-01-01
This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
The complex-mass scheme and unitarity in perturbative quantum field theory
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Denner, Ansgar; Lang, Jean-Nicolas [Universitaet Wuerzburg, Institut fuer Theoretische Physik und Astrophysik, Wuerzburg (Germany)
2015-08-15
We investigate unitarity within the complex-mass scheme, a convenient universal scheme for perturbative calculations involving unstable particles in quantum field theory which guarantees exact gauge invariance. Since this scheme requires one to introduce complex masses and complex couplings, the Cutkosky cutting rules, which express perturbative unitarity in theories of stable particles, are no longer valid. We derive corresponding rules for scalar theories with unstable particles based on Veltman's largest-time equation and prove unitarity in this framework. (orig.)
Functional integral method in quantum field theory of plasmons in graphene
Duoc Phan, Nguyen Duc; Hau Tran, Van
2017-12-01
In the present work we apply the functional integral method to the study of quantum field theory of collective excitations of spinless Dirac fermion in graphene at vanishing absolute temperature and at Fermi level {{E}F}=0 . After introducing the Hermitian scalar field \\varphi (x) describing these collective excitations we establish the expression of the functional integral {{Z}\\varphi } containing a functional series I[\\varphi ] . The explicit expressions of several terms of this functional series were derived. Then we consider the functional series I[\\varphi ] in second order approximation and denote {{I}0}[\\varphi ] the corresponding approximate expression of I[\\varphi ] . We shall demonstrate that in this approximation the scalar field \\varphi (x) can be devided into two parts: a background field {{\\varphi }0}(x) corresponding to the extremum of {{I}0}[\\varphi ] and another scalar field ξ (x) describing the fluctuation of \\varphi (x) around the background {{\\varphi }0}(x) . We call ξ (x) the fluctuation field. Then we establish the relationship between this fluctuation field ξ (x) and the quantum field of plasmons in graphene. Considering some range of values of frequency (energy) and wave vector (momentum) of plasmons, when the analytical calculations can be performed, we derived the differential equation for the quantum field of graphene plasmons. From this field equation we establish the relation between frequency and wave vector of plasmons in the long wavelength limit.
From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
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Jeon, S.; Yaffe, L.G. [Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
1996-05-01
The evaluation of hydrodynamic transport coefficients in relativistic field theory, and the emergence of an effective kinetic theory description, is examined. Even in a weakly coupled scalar field theory, interesting subtleties arise at high temperatures where thermal renormalization effects are important. In this domain, a kinetic theory description in terms of the fundamental particles ceases to be valid, but one may derive an effective kinetic theory describing excitations with temperature dependent properties. While the shear viscosity depends on the elastic scattering of typical excitations whose kinetic energies are comparable to the temperature, the bulk viscosity is sensitive to particle nonconserving processes at small energies. As a result, the shear and the bulk viscosities have very different dependence on the interaction strength and temperature, with the bulk viscosity providing an especially sensitive test of the validity of an effective kinetic theory description. {copyright} {ital 1996 The American Physical Society.}
Quasi-quantum groups, knots, three-manifolds, and topological field theory
Altschüler, D R; Altschuler, Daniel; Coste, Antoine
1992-01-01
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle $\\om$, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data $G, \\,\\om$.
Finite-temperature field theory and quantum noise in an electrical network
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Garavaglia, T.
1988-10-15
Finite-temperature (0less than or equal toT
Integrability of a family of quantum field theories related to sigma models
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Ridout, David [Australian National Univ., Canberra, ACT (Australia). Dept. of Theoretical Physics; DESY, Hamburg (Germany). Theory Group; Teschner, Joerg [DESY, Hamburg (Germany). Theory Group
2011-03-15
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2 vertical stroke 1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS{sub 2} x S{sup 2}, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Bossard, G
2007-10-15
This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the {beta} function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)
Schürmann, Michael
2008-01-01
This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.
Quantum Field Theory of Interacting Dark Matter/Dark Energy: Dark Monodromies
D'Amico, Guido; Kaloper, Nemanja
2016-11-28
We discuss how to formulate a quantum field theory of dark energy interacting with dark matter. We show that the proposals based on the assumption that dark matter is made up of heavy particles with masses which are very sensitive to the value of dark energy are strongly constrained. Quintessence-generated long range forces and radiative stability of the quintessence potential require that such dark matter and dark energy are completely decoupled. However, if dark energy and a fraction of dark matter are very light axions, they can have significant mixings which are radiatively stable and perfectly consistent with quantum field theory. Such models can naturally occur in multi-axion realizations of monodromies. The mixings yield interesting signatures which are observable and are within current cosmological limits but could be constrained further by future observations.
Quantum dynamics manipulation using optimal control theory in the presence of laser field noise
Kumar, Praveen; Malinovskaya, Svetlana A.
2010-08-01
We discuss recent advances in optimal control theory (OCT) related to the investigation of the impact of control field noise on controllability of quantum dynamics. Two numerical methods, the gradient method and the iteration method, are paid particular attention. We analyze the problem of designing noisy control fields to maximize the vibrational transition probability in diatomic quantum systems, e.g. the HF and OH molecules. White noise is used as an additive random variable in the amplitude of the control field. It is demonstrated that the convergence is faster in the presence of noise and population transfer is increased by 0.04% for small values of noise compared to the field amplitude.
Quantum field theories coupled to supergravity. AdS/CFT and local couplings
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Grosse, J.
2006-08-03
This dissertation is devoted to the investigation of the interplay of supersymmetric Yang-Mills theories (SYM) and supergravity (SUGRA). The topic is studied from two points of view: Firstly from the point of view of AdS/CFT correspondence, which realises the coupling of four dimensional superconformal N=4 SYM theory and ten dimensional type IIB SUGRA in a holographic way. In order to arrive at theories that resemble quantum chromodynamics (QCD) more closely, fundamental fields are introduced using probe D7-branes and nontrivial background configuration are considered. In particular supergravity solutions that are only asymptotically anti-de Sitter and break supersymmetry are used. This allows the description of spontaneous chiral symmetry breaking. The meson spectrum is calculated and the existence of an associated Goldstone mode is demonstrated. Moreover it is shown that highly radially excited mesons are not degenerate. Additionally instanton configurations on the D7-branes are investigated, which lead to a holographic description of the dual field theory's Higgs branch. Finally a holographic description of heavy-light mesons is developed, which are mesons consisting of quarks with a large mass difference, such that a treatment of B mesons can be achieved. The second approach to the topic of this thesis is the technique of socalled space-time dependent couplings (also known as ''local couplings''), where coupling constants are promoted to external sources. This allows to explore the conformal anomaly of quantum field theories coupled to a classical gravity background. The technique is extended to the superfield description of N=1 supergravity, a complete basis for the anomaly is given and the consistency conditions that arise from a cohomological treatment are calculated. Possible implications for an extension of Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field theories are discussed. (orig.)
Bucharest PhD Training School : Modern Aspects of Quantum Field Theory and Applications
2015-01-01
Bucharest 2015 – Modern Aspects of Quantum Field Theory is part of the CERN – SEENET-MTP PhD Training Program, which consists of a number of seminars in theoretical high energy Physics. This is the second seminar organized by this Program. Here are some photos from this event held in Bucharest between 8-14 November 2015. The previous seminar was organized in Belgrade, under the name Belgrade 2015 - Supergravity.
In–out propagator in de Sitter space from general boundary quantum field theory
Directory of Open Access Journals (Sweden)
Daniele Colosi
2015-09-01
Full Text Available The general boundary formulation of quantum theory is applied to quantize a real massive scalar field in de Sitter space. The space–time region where the dynamics of the field takes place is bounded by one spacelike hypersurface of constant conformal de Sitter time. The computation of the amplitude in the presence of a linear interaction with a source field with compact support in the region considered provides the expression of the Feynman propagator which coincides with the so-called in–out propagator.
Computer algebra in quantum field theory integration, summation and special functions
Schneider, Carsten
2013-01-01
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including
Resurgence in Quantum Field Theory: Nonperturbative Effects in the Principal Chiral Model
Cherman, Aleksey; Dorigoni, Daniele; Dunne, Gerald V.; Ünsal, Mithat
2014-01-01
We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory. These points are illustrated in the PCM, where we find new nonperturbative "fracton" saddle point field configurations, and suggest a quantum interpretation of previously discovered "uniton" unstable classical solutions. The fractons lead to a semiclassical realization of IR renormalons in the circle-compactified theory and yield the microscopic mechanism of the mass gap of the PCM.
Variational methods for field theories
Energy Technology Data Exchange (ETDEWEB)
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Gürdoğan, Ömer; Kazakov, Vladimir
2016-11-11
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ-deformed N=4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the 't Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS/CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N=4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
On the Question of the Scattering Matrix in Quantum Field Theory
Khokhlov, I. A.
2017-06-01
A new expression for the scattering matrix in local quantum field theory is obtained on the basis of a generalized formulation of the microcausality condition. This expression is relativistically covariant, unitary, and causal and coincides with the generally accepted expression (the T-exponential) in the case when ultraviolet (UV) divergences are absent in the latter. Conditions are formulated, under the fulfillment of which the elements of the constructed matrix do not contain UV divergences. By way of an example, the probability amplitude of the particle-particle transition for a model with ℒ( x) = λ : φ 3( x): in the second-order perturbation theory is found.
Quantum information theory mathematical foundation
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...
Pascual Jordan's legacy and the ongoing research in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert, E-mail: schroer@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik
2010-02-15
After recalling Pascual Jordan's path breaking work in shaping quantum mechanics I explain his role as the protagonist of quantum field theory (QFT). Particular emphasis is given to the 1929 Kharkov conference where Jordan not only presents a quite modern looking panorama about the state of art, but were some of his ideas already preempt an intrinsic point of view about a future QFT liberated from the classical parallelism and quantum field theory, a new approach for which the conceptional basis began to emerge only 30 years later. Two quite profound subjects in which Jordan was far ahead of his contemporaries will be presented in separate sections: 'Bosonization and Re-fermionization instead of Neutrino theory of Light' and 'Nonlocal gauge invariants and an algebraic monopole quantization'. The last section contains scientific episodes mixed with biographical details. It includes remarks about his much criticized conduct during the NS regime. Without knowing about his entanglement with the Nazis it is not possible to understand that such a giant of particle physics dies without having received a Nobel prize. (author)
Quantum kinetic theory of metal clusters in an intense electromagnetic field
Directory of Open Access Journals (Sweden)
M.Bonitz
2004-01-01
Full Text Available A quantum kinetic theory for weakly inhomogeneous charged particle systems is derived within the framework of nonequilibrium Green's functions. The results are of relevance for valence electrons of metal clusters as well as for confined Coulomb systems, such as electrons in quantum dots or ultracold ions in traps and similar systems. To be specific, here we concentrate on the application to metal clusters, but the results are straightforwardly generalized. Therefore, we first give an introduction to the physics of correlated valence electrons of metal clusters in strong electromagnetic fields. After a brief overview on the jellium model and the standard density functional approach to the ground state properties, we focus on the extension of the theory to nonequilibrium. To this end a general gauge-invariant kinetic theory is developed. The results include the equations of motion of the two-time correlation functions, the equation for the Wigner function and an analysis of the spectral function. Here, the concept of an effective quantum potential is introduced which retains the convenient local form of the propagators. This allows us to derive explicit results for the spectral function of electrons in a combined strong electromagnetic field and a weakly inhomogeneous confinement potential.
Pascal Jordan's legacy and the ongoing research in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Institut fuer Theoretische Physik der FU Berlin (Germany)], e-mail: schroer@cbpf.br
2010-07-01
After recalling Pascual Jordan's path breaking work in shaping quantum mechanics I explain his role as the protagonist of quantum field theory (QFT). Particular emphasis is given to the 1929 Kharkov conference where Jordan not only presents a quite modern looking panorama about the state of art, but were some of his ideas already preempt an intrinsic point of view about a future QFT liberated from the classical parallelism and quantum field theory, a new approach for which the conceptional basis began to emerge only 30 years later. Two quite profound subjects in which Jordan was far ahead of his contemporaries will be presented in separate sections: 'Bosonization and Re-fermionization instead of Neutrino theory of Light' and {sup N}onlocal gauge invariants and an algebraic monopole quantization{sup .} The last section contains scientific episodes mixed with biographical details. It includes remarks about his much criticized conduct during the NS regime. Without knowing about his entanglement with the Nazis it is not possible to understand that such a giant of particle physics dies without having received a Nobel prize. (author)
Effective field theory for the quantum electrodynamics of a graphene wire
Faccioli, P.; Lipparini, E.
2009-07-01
We study the low-energy quantum electrodynamics of electrons and holes in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/pT , where pT is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest order in (p/pT) , our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound states, and we calculate the dispersion law of such modes. We also compute the dc conductivity per unit length at zero chemical potential and find gs(e2)/(h) , where gs=4 is the degeneracy factor.
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
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Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
Peierls, Rudolf Ernst
1955-01-01
This book develops the subject from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to be used and care is taken to separate sound arguments from conjecture. This book is written for the student of theoretical physics who wants to work in the field of solids and for the experimenter with a knowledge of quantum theory who is not content to take other people's arguments for granted. The treatment covers the electron theory of metals as well as the dynamics of crystals, including the author's work on the thermal conductivity of crystals which has been previously published in English.
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
On the Stability of KMS States in Perturbative Algebraic Quantum Field Theories
Drago, Nicolò; Faldino, Federico; Pinamonti, Nicola
2017-08-01
We analyze the stability properties shown by KMS states for interacting massive scalar fields propagating over Minkowski spacetime, recently constructed in the framework of perturbative algebraic quantum field theories by Fredenhagen and Lindner (Commun Math Phys 332:895, 2014). In particular, we prove the validity of the return to equilibrium property when the interaction Lagrangian has compact spatial support. Surprisingly, this does not hold anymore, if the adiabatic limit is considered, namely when the interaction Lagrangian is invariant under spatial translations. Consequently, an equilibrium state under the adiabatic limit for a perturbative interacting theory evolved with the free dynamics does not converge anymore to the free equilibrium state. Actually, we show that its ergodic mean converges to a non-equilibrium steady state for the free theory.
Quantum field theory as effective BV theory from Chern-Simons
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Krotov, Dmitry [Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow 117312 (Russian Federation); Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117259 (Russian Federation); Moscow State University, Department of Physics, Vorobjevy Gory, Moscow 119899 (Russian Federation)], E-mail: krotov@itep.ru; Losev, Andrei [Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117259 (Russian Federation)
2009-01-11
The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern-Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of 'singular' point from the perspective of the suggested method for cohomology evaluation. For arbitrary 'regular' point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern-Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, (hep-th/0105050); N. Berkovits, ICTP lectures on covariant quantization of the superstring, (hep-th/0209059); M. Movshev, A. Schwarz, On maximally supersymmetric Yang-Mills theories, Nucl. Phys. B 681 (2004) 324, (hep-th/0311132); M. Movshev, A. Schwarz, Algebraic structure of Yang-Mills theory, (hep-th/0404183)].
Irreversibility of the renormalization group flow in non-unitary quantum field theory
Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Ravanini, Francesco
2017-10-01
We show irreversibility of the renormalization group flow in non-unitary but {{ P}T} -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s c-theorem to {{ P}T} -symmetric Hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is non-negative and monotonically decreasing along renormalization group flows. Its value at a critical point is the ‘effective central charge’ entering the specific free energy. At least in rational models, this equals ceff=c-24Δ , where c is the central charge and Δ is the lowest primary field dimension in the conformal field theory which describes the critical point. Dedicated to John Cardy on the occasion of his 70th birthday.
Worldline approach to quantum field theories on flat manifolds with boundaries
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.
2006-01-01
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1} extends to a potential which gen...
Towards the Construction of Quantum Field Theories from a Factorizing S-Matrix
Lechner, Gandalf
Starting from a given factorizing S-matrix S in two space-time dimensions, we review a novel strategy to rigorously construct quantum field theories describing particles whose interaction is governed by S. The construction procedure is divided into two main steps: Firstly certain semi-local Wightman fields are introduced by means of Zamolodchikov's algebra. The second step consists in proving the existence of local observables in these models. As a new result, an intermediate step in the existence problem is taken by proving the modular compactness condition for wedge algebras.
Quantum field theory I foundations and Abelian and non-Abelian gauge theories
Manoukian, Edouard B
2016-01-01
This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Pa...
Quantum biological information theory
Djordjevic, Ivan B
2016-01-01
This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects. Integrates quantum information and quantum biology concepts; Assumes only knowledge of basic concepts of vector algebra at undergraduate level; Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology; Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models o...
Quantum Hall states and conformal field theory on a singular surface
Can, T.; Wiegmann, P.
2017-12-01
In Can et al (2016 Phys. Rev. Lett. 117), quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone (Cardy and Peschel 1988 Nucl. Phys. B 300 377–92), and the known results for critical systems on polyhedra and flat branched Riemann surfaces.
Raedt, Hans De; Binder, K; Ciccotti, G
1996-01-01
The purpose of this set of lectures is to introduce the general concepts that are at the basis of the computer simulation algorithms that are used to study the behavior of condensed matter quantum systems. The emphasis is on the underlying concepts rather than on specific applications. Topics
Morgenstern Horing, Norman J
2017-01-01
This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...
Unification of gravity and quantum field theory from extended noncommutative geometry
Yu, Hefu; Ma, Bo-Qiang
2017-02-01
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.
Holographic effective field theories
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Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' , Università di Padova,and INFN - Sezione di Padova, Via Marzolo 8, I-35131 Padova (Italy); Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,and INFN - Sezione di Milano-Bicocca, I-20126 Milano (Italy)
2016-06-28
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
HILBERT-PÓLYA Conjecture, Zeta Functions and Bosonic Quantum Field Theories
Andrade, Julio C.
2013-07-01
The original Hilbert and Pólya conjecture is the assertion that the nontrivial zeros of the Riemann zeta function can be the spectrum of a self-adjoint operator. So far no such operator was found. However, the suggestion of Hilbert and Pólya, in the context of spectral theory, can be extended to approach other problems and so it is natural to ask if there is a quantum mechanical system related to other sequences of numbers which are originated and motivated by Number Theory. In this paper, we show that the functional integrals associated with a hypothetical class of physical systems described by self-adjoint operators associated with bosonic fields whose spectra is given by three different sequence of numbers cannot be constructed. The common feature of the sequence of numbers considered here, which causes the impossibility of zeta regularizations, is that the various Dirichlet series attached to such sequences — such as those which are sums over "primes" of (norm P)-s have a natural boundary, i.e. they cannot be continued beyond the line Re(s) = 0. The main argument is that once the regularized determinant of a Laplacian is meromorphic in s, it follows that the series considered above cannot be a regularized determinant. In other words, we show that the generating functional of connected Schwinger functions of the associated quantum field theories cannot be constructed.
Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
Roberts, Daniel A.; Swingle, Brian
2016-08-01
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound—the Lieb-Robinson bound—and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity vB . Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that vB is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that vB remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.
Buchhold, Michael; Everest, Benjamin; Marcuzzi, Matteo; Lesanovsky, Igor; Diehl, Sebastian
2017-01-01
Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has proved a rather stringent requirement in experiments. Recently, a proposal to seek such transitions in highly tunable systems of cold-atomic gases offers to probe this physics and, at the same time, to investigate the robustness of these transitions to quantum coherent effects. Here, we specifically focus on the interplay between classical and quantum fluctuations in a simple driven open quantum model which, in the classical limit, reproduces a contact process, which is known to undergo a continuous transition in the "directed percolation" universality class. We derive an effective long-wavelength field theory for the present class of open spin systems and show that, due to quantum fluctuations, the nature of the transition changes from second to first order, passing through a bicritical point which appears to belong instead to the "tricritical directed percolation" class.
Comment on "Observer dependence of quantum states in relativistic quantum field theories"
Bloch, I.
1984-04-01
In response to Malin's recent paper it is suggested that the important aspect of timing in relativistic descriptions of position determinations is the timing with which a pure state is converted to a mixture, rather than the timing of the mixture's reduction to a new pure state; this suggestion removes some of the subjectivism that Malin finds in quantum states. It is suggested also that viewing quantum mechanics as a branch of psychology raises more questions than it answers.
Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán
2013-01-01
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Directory of Open Access Journals (Sweden)
Ryan eBabbush
2013-10-01
Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
PREFACE: Quantum Field Theory Under the Influence of External Conditions (QFEXT07)
Bordag, M.; Mostepanenko, V. M.
2008-04-01
This special issue contains papers reflecting talks presented at the 8th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT07), held on 17 21 September 2007, at Leipzig University. This workshop gathered 108 physicists and mathematicians working on problems which are focused on the following topics: •Casimir and van der Waals forces—progress in theory and new experiments, applications at micro- and nano-scale •Casimir effect—exact results, approximate methods and mathematical problems •Vacuum quantum effects in classical background fields—renormalization issues, singular backgrounds, applications to particle and high energy physics •Vacuum energy and gravity, vacuum energy in supersymmetric and noncommutative theories. This workshop is part of a series started in 1989 and 1992 in Leipzig by Dieter Robaschik, and continued in 1995, 1998 and 2001 in Leipzig by Michael Bordag. In 2003 this Workshop was organized by Kimball A Milton in Oklahoma, in 2005 by Emilio Elizalde in Barcelona and in 2007 it returned to Leipzig. The field of physics after which this series of workshops is named is remarkably broad. It stretches from experimental work on the measurement of dispersion forces between macroscopic bodies to quantum corrections in the presence of classical background fields. The underlying physical idea is that even in its ground state (vacuum) a quantum system responds to changes in its environment. The universality of this idea makes the field of its application so very broad. The most prominent manifestation of vacuum energy is the Casimir effect. This is, in its original formulation, the attraction between conducting planes due to the vacuum fluctuations of the electromagnetic field. In a sense, this is the long-range tail of the more general dispersion forces acting between macroscopic bodies. With the progress in nanotechnology, dispersion forces become of direct practical significance. On a more theoretical side
Quantum Self-Frictional Relativistic Nucleoseed Spinor-Type Tensor Field Theory of Nature
Directory of Open Access Journals (Sweden)
I. I. Guseinov
2017-01-01
Full Text Available For study of quantum self-frictional (SF relativistic nucleoseed spinor-type tensor (NSST field theory of nature (SF-NSST atomic-molecular-nuclear and cosmic-universe systems we use the complete orthogonal basis sets of 22s+1-component column-matrices type SF Ψnljmjδ⁎s-relativistic NSST orbitals (Ψδ⁎s-RNSSTO and SF Xnljmjs-relativistic Slater NSST orbitals (Xs-RSNSSTO through the ψnlmlδ⁎-nonrelativistic scalar orbitals (ψδ⁎-NSO and χnlml-nonrelativistic Slater type orbitals (χ-NSTO, respectively. Here δ⁎=pl⁎ or δ⁎=α⁎ and pl⁎=2l+2-α⁎, α⁎ are the integer (α⁎=α, -∞<α≤2 or noninteger (α⁎≠α, -∞<α⁎<3 SF quantum numbers, where s=0,1/2,1,3/2,2,…. We notice that the nonrelativistic ψδ⁎-NSO and χ-NSTO orbitals themselves are obtained from the relativistic Ψδ⁎s-RNSSTO and Xs-RSNSSTO functions for s=0, respectively. The column-matrices-type SF Y1jmjls-RNSST harmonics (Y1ls-RNSSTH and Y2jmjls-modified NSSTH (Y2ls-MNSSTH functions for arbitrary spin s introduced by the author in the previous papers are also used. The one- and two-center one-range addition theorems for ψδ⁎-NSO and noninteger n χ-NSTO orbitals are presented. The quantum SF relativistic nonperturbative theory for Vnljmjδ⁎-RNSST potentials (Vδ⁎-RNSSTP and their derivatives is also suggested. To study the transportations of mass and momentum in nature the quantum SF relativistic NSST gravitational photon (gph with s=1 is introduced.
Controlling the sign problem in finite-density quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Garron, Nicolas; Langfeld, Kurt [University of Liverpool, Theoretical Physics Division, Department of Mathematical Sciences, Liverpool (United Kingdom)
2017-07-15
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the ''telegraphic'' approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign-problem regime. (orig.)
Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories
Alazzawi, Sabina; Lechner, Gandalf
2017-09-01
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.
Quantum theory of chemical reactions in the presence of electromagnetic fields.
Tscherbul, T V; Krems, R V
2008-07-21
We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Water Bridging Dynamics of Polymerase Chain Reaction in the Gauge Theory Paradigm of Quantum Fields
Directory of Open Access Journals (Sweden)
L. Montagnier
2017-05-01
Full Text Available We discuss the role of water bridging the DNA-enzyme interaction by resorting to recent results showing that London dispersion forces between delocalized electrons of base pairs of DNA are responsible for the formation of dipole modes that can be recognized by Taq polymerase. We describe the dynamic origin of the high efficiency and precise targeting of Taq activity in PCR. The spatiotemporal distribution of interaction couplings, frequencies, amplitudes, and phase modulations comprise a pattern of fields which constitutes the electromagnetic image of DNA in the surrounding water, which is what the polymerase enzyme actually recognizes in the DNA water environment. The experimental realization of PCR amplification, achieved through replacement of the DNA template by the treatment of pure water with electromagnetic signals recorded from viral and bacterial DNA solutions, is found consistent with the gauge theory paradigm of quantum fields.
Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes
Solveen, Christoph
2010-01-01
The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.
Local thermal equilibrium in quantum field theory on flat and curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Solveen, Christoph, E-mail: Christoph.Solveen@theorie.physik.uni-goettingen.d [Institut fuer Theoretische Physik, Universitaet Goettingen, Friedrich-Hund-Platz 1, 37077 Goettingen (Germany)
2010-12-07
The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Energy Technology Data Exchange (ETDEWEB)
Ellis, R. Keith [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Kunszt, Zoltan [Institute for Theoretical Physics (Switzerland); Melnikov, Kirill [Johns Hopkins Univ., Baltimore, MD (United States); Zanderighi, Giulia [Rudolf Peierls Centre for Theoretical Physics (United Kingdom)
2012-09-01
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
General properties of the n-point functions in local quantum field theory
Epstein, H; Stora, Raymond Félix
1976-01-01
One of the most satisfactory aspects of relativistic local quantum field theory is the asymptotic theory of Haag and Ruelle: starting from a few simple hypotheses (locality, relativistic invariance, and spectrum, including the explicit exclusion of zero-mass states) the existence of the scattering operator S and of scattering amplitudes is established: these amplitudes can then be expressed through the 'reduction formulae' of L.S.Z. (rigorously proved in the framework of the Haag-Ruelle theory by Hepp for Wightman fields, and by Araki for bounded local observables) as the restrictions to the mass-shell of the Fourier transforms of (amputated) chronological functions. The latter, through the interplay of locality and spectrum, can be shown to be boundary values of certain analytic functions (Green functions), and this is the origin of analyticity properties of the scattering amplitudes. The purpose of these lectures is to set the scene for the study of such analyticity properties by giving a description of the...
Examples of reflection positive field theories
Trinchero, R.
The requirement of reflection positivity (RP) for Euclidean field theories is considered. This is done for the cases of a scalar field, a higher derivative scalar field theory and the scalar field theory defined on a non-integer dimensional space (NIDS). It is shown that regarding RP, the analytical structure of the corresponding Schwinger functions plays an important role. For the higher derivative scalar field theory, RP does not hold. However for the scalar field theory on a NIDS, RP holds in a certain range of dimensions where the corresponding Minkowskian field is defined on a Hilbert space with a positive definite scalar product that provides a unitary representation of the Poincaré group. In addition, and motivated by the last example, it is shown that, under certain conditions, one can construct non-local reflection positive Euclidean field theories starting from the corrected two point functions of interacting local field theories.
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Quantum field theory and the linguistic Minimalist Program: a remarkable isomorphism
Piattelli-Palmarini, M.; Vitiello, G.
2017-08-01
By resorting to recent results, we show that an isomorphism exist between linguistic features of the Minimalist Program and the quantum field theory formalism of condensed matter physics. Specific linguistic features which admit a representation in terms of the many-body algebraic formalism are the unconstrained nature of recursive Merge, the operation of the Labeling Algorithm, the difference between pronounced and un-pronounced copies of elements in a sentence and the build-up of the Fibonacci sequence in the syntactic derivation of sentence structures. The collective dynamical nature of the formation process of Logical Forms leading to the individuation of the manifold of concepts and the computational self-consistency of languages are also discussed.
Braided Categories of Endomorphisms as Invariants for Local Quantum Field Theories
Giorgetti, Luca; Rehren, Karl-Henning
2017-08-01
We want to establish the "braided action" (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field theories. The environment algebra can either be a single local algebra, or the quasilocal algebra, both of which are model-independent up to isomorphism. The DHR category as an abstract structure is captured by finitely many data (superselection sectors, fusion, and braiding), whereas its braided action encodes the full dynamical information that distinguishes models with isomorphic DHR categories. We show some geometric properties of the "duality pairing" between local algebras and the DHR category that are valid in general (completely rational) chiral CFTs. Under some additional assumptions whose status remains to be settled, the braided action of its DHR category completely classifies a (prime) CFT. The approach does not refer to the vacuum representation, or the knowledge of the vacuum state.
Thermalization and revivals after a quantum quench in conformal field theory.
Cardy, John
2014-06-06
We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature β≪L. For times t such that ℓ/2modular transformations. At early times t≪(Lβ)^{1/2} there is a universal decay F∼exp(-(πc/3)Lt^{2}/β(β^{2}+4t^{2})). The effect of an irrelevant nonintegrable perturbation of the CFT is to progressively broaden each revival at t=nL/2 by an amount O(n^{1/2}).
Kleinert, Hagen
2016-01-01
This is an introductory book on elementary particles and their interactions. It starts out with many-body Schrödinger theory and second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The latter is an outcome of the Feynman-Kleinert variational approach to path integrals discussed in two earlier books of the author, one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordin...
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Yuriy [North Carolina State Univ., Raleigh, NC (United States)
2004-12-01
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
Reduction of Couplings in Quantum Field Theories with applications in Finite Theories and the MSSM
Heinemeyer, S; Tracas, N; Zoupanos, G
2014-01-01
We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. It has a remarkable predictive power since, at the unification scale, it leads to relations between gauge and Yukawa couplings in the dimensionless sectors and relations involving the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the unified gaugino mass in the soft breaking sector. In both the MSSM and the FUT model we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Furthermore we also predict the masses of the other Higgses, as well as the supersymmetric spectrum, both being in very confortable agreement with the LHC bounds on Higgs and supersymmetric particles.
A new ordering principle in quantum field theory and its consequences
Greben, Jan M
2016-01-01
The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentum tensor and currents is a standard tool in quantum field theory (QFT) to eliminate infinite vacuum expectation values (v.e.v.) However, for fermionic expressions these infinite terms are due to anti-particles only. This exposes an asymmetry in standard QFT, which can be traced back to a bias towards particles in the Dirac bra-ket notation. To counter this bias a new ordering principle (called the $\\mathbb{R}$-product) is required which restores the symmetry (or rather duality) between particles and anti-particles and eliminates the infinite v.e.v. While this $\\mathbb{R}$-product was already used in a bound-state application, this paper aims to give it a more general foundation and analyze its overall impact in QFT. For boson fields the particle bias is hidden and the fields must first be expanded into bilinear particle-anti-particle fermion operators. This new representation also leads to vanishing v.e.v.'s and avoids some common techn...
Effective spacetime understanding emergence in effective field theory and quantum gravity
Crowther, Karen
2016-01-01
This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop quantum gravity.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Roman, Steven
2006-01-01
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been im
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
Holographic description of curved-space quantum field theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Uhlemann, Christoph Frank
2012-12-12
The celebrated AdS/CFT dualities provide a window to strongly-coupled quantum field theories (QFTs), which are realized in nature at the most fundamental level on the one hand, but are hardly accessible for the standard mathematical tools on the other hand. The prototype examples of AdS/CFT relate classical supergravity theories on (d+1)-dimensional anti-de Sitter space (AdS) to strongly-coupled d-dimensional conformal field theories (CFTs). The AdS spacetimes admit a timelike conformal boundary, on which the dual CFT is defined. In that sense the AdS/CFT dualities are holographic, and this new approach has led to remarkable progress in understanding strongly-coupled QFTs defined on Minkowski space and on the Einstein cylinder. On the other hand, the study of QFT on more generic curved spacetimes is of fundamental interest and non-trivial already for free theories. Moreover, understanding the properties of gravity as a quantum theory remains among the hardest problems to solve in physics. Both of these issues can be studied holographically and we investigate here generalizations of AdS/CFT involving on the lower-dimensional side QFTs on curved backgrounds and as a further generalization gravity. In the first part we expand on the holographic description of QFT on fixed curved backgrounds, which involves gravity on an asymptotically-AdS space with that prescribed boundary structure. We discuss geometries with de Sitter and AdS as conformal boundary to holographically describe CFTs on these spacetimes. After setting up the procedure of holographic renormalization we study the reflection of CFT unitarity properties in the dual bulk description. The geometry with AdS on the boundary exhibits a number of interesting features, mainly due to the fact that the boundary itself has a boundary. We study both cases and resolve potential tensions between the unitarity properties of the bulk and boundary theories, which would be incompatible with a duality. The origin of these
New Constraints on Quantum Theories
Directory of Open Access Journals (Sweden)
Comay E.
2013-04-01
Full Text Available Hierarchical relationships between physical theories are discussed. It is explained how a lower rank theory imposes constraints on an acceptable structure of its higher rank theory. This principle is applied to the case of quantum mechanics and quantum field theory of massive particles. It is proved that the Dirac equation is consistent with these constraints whereas the Klein-Gordon equation, as well as all other second order quan- tum equations are inconsistent with the Schrödinger equation. This series of arguments undermines the theoretical structure of the Standard Model.
Bochicchio, Marco
2015-03-01
We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse-Smale-Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang-Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in (1)/(N), a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a
Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-05
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Dual gauge field theory of quantum liquid crystals in three dimensions
Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai; Zaanen, Jan
2017-10-01
The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. We also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.
Fewster, Christopher J
2015-08-06
The framework of locally covariant quantum field theory is discussed, motivated in part using 'ignorance principles'. It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be expressed via natural isomorphisms between the corresponding functors. The inhomogeneous scalar field is used to illustrate the ideas. It is argued that there are two reasonable definitions of the local physical content associated with a locally covariant theory; when these coincide, the theory is said to be dynamically local. The status of the dynamical locality condition is reviewed, as are its applications in relation to (i) the foundational question of what it means for a theory to represent the same physics in different space-times and (ii) a no-go result on the existence of natural states. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Franklin, Joel
2017-01-01
Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...
1999-11-08
In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, Claudio, E-mail: claudio.dappiaggi@unipv.it; Nosari, Gabriele [Università degli Studi di Pavia, Dipartimento di Fisica (Italy); Pinamonti, Nicola [Università di Genova, Dipartimento di Matematica (Italy)
2016-06-15
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
Wilde, Mark M
2017-01-01
Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theo...
Quantum field theory and the antipodal identification of black-holes
Sanchez, N.; Whiting, B. F.
The antipodal points (U, V, θ, ϕ) and (-U, -V, π - θ, ϕ + π) of the Schwarzchild-Kruskal manifold, usually interpreted as two different events (in two different worlds) are considered here as physically identified (to give one single world). This has fundamental consequences for the QFT formulated on this manifold. The antipodal symmetric fields have (globally) zero norm. The usual particle-antiparticle Fock space definition breaks down. There is no quantum operator (unitary, antiunitary or projection) giving antipodal symmetric states from the usual Kruskal ones. The antipodal symmetric Green functions have the same periodicity β = 8 π M in imaginary (Schwarzschild) time as the usual (non-symmetric) ones. (Identification with ``conical singularity'' would give a period 1/2β). In any case, no usual thermal interpretation is possible for T = β-1 (nor for T0 = 2/β or any other value) in the theory. In the light of these results we discuss ``old'' ideas and more recent ones on identification. Present address: Department of Physics and Astronomy, University of North Carolina-Chapel Hill, NC 27514, USA.
Altland, Alexander; Simons, Ben
2006-06-01
Over the past few decades, in concert with ground-breaking experimental advances, condensed matter theory has drawn increasingly from the language of low-energy quantum field theory. This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. It emphasizes the development of modern methods of classical and quantum field theory with applications oriented around condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking. This book will complement graduate level courses on theoretical quantum condensed matter physics. Spans the field of modern condensed matter theory focusing on field theory techniques Written to facilitate learning, with numerous challenging exercises, with fully worked solutions, aimed at physicists starting graduate-level courses The theoretical methods are firmly set in concrete experimental applications
Conformal Janus on Euclidean sphere
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu [Physics Department, University of Seoul,Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences,Daejeon 34047 (Korea, Republic of); Gustavsson, Andreas [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of); Rey, Soo-Jong [School of Physics & Astronomy and Center for Theoretical Physics,Seoul National University,Seoul 08826 (Korea, Republic of); Center for Theoretical Physics, College of Physical Sciences, Sichuan University,Chengdu 610064 P.R. (China); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences,Daejeon 34047 (Korea, Republic of)
2016-12-07
We interpret Janus as an interface in a conformal field theory and study its properties. The Janus is created by an exactly marginal operator and we study its effect on the interface conformal field theory on the Janus. We do this by utilizing the AdS/CFT correspondence. We compute the interface free energy both from leading correction to the Euclidean action in the dual gravity description and from conformal perturbation theory in the conformal field theory. We find that the two results agree each other and that the interface free energy scales precisely as expected from the conformal invariance of the Janus interface.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, R.
2007-03-15
The present work is addressed to defects and boundaries in quantum field theory considering the application to AdS/CFT correspondence. We examine interactions of fermions with spins localised on these boundaries. Therefore, an algebra method is emphasised adding reflection and transmission terms to the canonical quantisation prescription. This method has already been applied to bosons in two space-time dimensions before. We show the possibilities of such reflection-transmission algebras in two, three, and four dimensions. We compare with models of solid state physics as well as with the conformal field theory approach to the Kondo effect. Furthermore, we discuss ansatzes of extensions to lattice structures. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki [Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526 (Japan); Tomsk state Pedagogical University Tomsk 634041 (Russian Federation)
2012-07-27
We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.
Broken symmetries in field theory
Kok, Mark Okker de
2008-01-01
The thesis discusses the role of symmetries in Quantum Field Theory. Quantum Field Theory is the mathematical framework to describe the physics of elementary particles. A symmetry here means a transformation under which the model at hand is invariant. Three types of symmetry are distinguished: 1.
Reaction-rate formula in out of equilibrium quantum field theory
Niegawa, A.; Okano, K.; Ozaki, H.
1999-01-01
A complete derivation, from first principles, of the reaction-rate formula for a generic reaction taking place in an out of equilibrium quantum-field system is given. It is shown that the formula involves no finite-volume correction. Each term of the reaction-rate formula represents a set of physical processes that contribute to the reaction under consideration.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, F
1999-01-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived f...
Directory of Open Access Journals (Sweden)
Jérôme Dubail, Jean-Marie Stéphan, Jacopo Viti, Pasquale Calabrese
2017-02-01
Full Text Available Conformal field theory (CFT has been extremely successful in describing large-scale universal effects in one-dimensional (1D systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system's inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means.
"Loops and Legs in Quantum Field Theory", 12th DESY Workshop on Elementary Particle Physics
The bi-annual international conference "Loops and Legs in Quantum Field Theory" has been held at Weimar, Germany, from April 27 to May 02, 2014. It has been the 12th conference of this series, started in 1992. The main focus of the conference are precision calculations of multi- loop and multi-leg processes in elementary particle physics for processes at present and future high-energy facilities within and beyond the Standard Model. At present many physics questions studied deal with processes at the LHC and future facilities like the ILC. A growing number of contributions deals with important developments in the field of computational technologies and algorithmic methods, including large-scale computer algebra, efficient methods to compute large numbers of Feynman diagrams, analytic summation and integration methods of various kinds, new related function spaces, precise numerical methods and Monte Carlo simulations. The present conference has been attended by more than 110 participants from all over the world, presenting more than 75 contributions, most of which have been written up for these pro- ceedings. The present volume demonstrates in an impressive way the enormous development of the field during the last few years, reaching the level of 5-loop calculations in QCD and a like- wise impressive development in massive next-to-leading order and next-to-next-to-leading order processes. Computer algebraic and numerical calculations require terabyte storage and many CPU years, even after intense parallelization, to obtain state-of-the-art theoretical predictions. The city of Weimar gave a suitable frame to the conference, with its rich history, especially in literature, music, arts, and architecture. Goethe, Schiller, Wieland, Herder, Bach and Liszt lived there and created many of their masterpieces. The many young participants signal that our field is prosperous and faces an exciting future. The conference hotel "Kaiserin Augusta" offered a warm hospitality and
The development of elementary quantum theory
Capellmann, Herbert
2017-01-01
This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics. Drawing on original publications and letters written by the main protagonists of that time, it shows that Einstein’s contributions from 1905 to 1924 laid the essential foundations for the development of Quantum Theory. Einstein introduced quantization of the radiation field; Born added quantized mechanical behavior. In addition, Born recognized that Quantum Mechanics necessarily required Quantum Optics; his radical concept of truly discontinuous and statistical quantum transitions (“quantum leaps”) was directly based on Einstein’s physical concepts.
Energy Technology Data Exchange (ETDEWEB)
Morales Villasevil, A.
1965-07-01
A method is introduced ta deal with relativistic quantum field theory for particles with m=0. Two mappings I and J, giving rise respectively to particle and anti particle states, are defined between a test space and the physical Hilbert space. The intrinsic field operator is then defined as the minimal causal linear combinations of operators belonging to the annihilation-creation algebra associated to the germ and antigerm parts of the element. Local elements are introduced as improper test elements and local field operators are constructed in the same way as the intrinsic ones. Commutation rules are given. (Author) 17 refs.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, F.
1999-05-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory.
Burgess, Cliff P
2004-01-01
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
Portrait of Gunnar Källén a physics shooting star and poet of early quantum field theory
2014-01-01
Wolfgang Pauli referred to him as 'my discovery,' Robert Oppenheimer described him as 'one of the most gifted theorists' and Niels Bohr found him enormously stimulating. Who was the man in question, Gunnar Källén (1926-1968)? His appearance in the physics sky was like a shooting star. His contributions to the scientific debate caused excitement among young and old. Similar to his friend and mentor, Wolfgang Pauli, he demanded honesty and rigor in physics - a distinct dividing line between fact and speculation. In his obituary, Arthur S. Wightman would write: 'Gunnar Källén was a proud continuer of the tradition in quantum field theory established by Wolfgang Pauli. His papers on quantum electrodynamics in the period 1950-1954 carried the non-perturbative approach to quantum electrodynamics forward to a point beyond which very little essential progress has been made up to the present day. At the time I was trying to puzzle out the grammar of the language of quantum field theory, and here was Källén al...
Directory of Open Access Journals (Sweden)
Marco Panero
2006-11-01
Full Text Available We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Friedberg, R; Hohenberg, P C
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory
On dynamical mass generation in Euclidean de Sitter space
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Moch, Paul; Beneke, Martin [Physik Department T31, Technische Universitaet Muenchen (Germany); Institut fuer Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University (Germany)
2013-07-01
We consider the perturbative treatment of a minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing the work of Rajaraman, we obtain the dynamical mass m{sup 2}∝√(λ)H{sup 2} of the scalar for non-vanishing Lagrangian masses and the first perturbative quantum correction in the massless case. We introduce the rules of a systematic perturbative expansion, which treats the zero-mode non-perturbatively, and goes in powers of √(λ). The infrared divergences of the massless free field theory are self-regulated by the zero-mode dynamics. Thus, in Euclidean de Sitter space the interacting and massless scalar field is just as well-defined as the massive field. We then show that the dynamical mass can be recovered from the diagrammatic expansion of the self-energy and a consistent solution of the Schwinger-Dyson equation. This requires the summation of a divergent series of loop diagrams of arbitrarily high order. We note that the value of the long-wavelength mode two-point function in Euclidean de Sitter space agrees at leading order with the stochastic treatment in Lorentzian de Sitter space, in any number of dimensions.
Angular momentum conservation law in light-front quantum field theory
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Chiu, Kelly Yu-Ju; Brodsky, Stanley J.; /SLAC /Stanford U.
2017-03-01
We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.
Renormalization and effective field theory
Costello, Kevin
2011-01-01
This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in "mathematics" itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. --Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. --Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorio...
Wieser, R
2017-05-04
A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.
Chord diagrams, contact-topological quantum field theory, and contact categories
Mathews, Daniel
In this thesis we study some interesting mathematics arising at the intersection of the studies of contact topology and sutured Floer homology. Although this work was originally motivated by the study of contact elements in sutured Floer homology, we also obtain results in pure contact topology. We consider contact elements in the sutured Floer homology of solid tori, as part of the (1+1)-dimensional topological quantum field theory defined by Honda-Kazez-Matic. We find that the Z2 sutured Floer homology of solid tori with longitudinal sutures forms a "categorification of Pascal's triangle", a triangle of vector spaces. Contact structures on solid tori with longitudinal sutures correspond bijectively to chord diagrams, which are sets of disjoint properly embedded arcs in the disc; these may in turn be identified with contact elements. The contact elements form distinguished subsets of the vector spaces in the categorified Pascal's triangle, of order given by the Narayana numbers. We find natural "creation and annihilation operators" which allow us to define a QFT-type basis of each SFH vector space, consisting of contact elements. We show that sutured Floer homology in this case reduces to the combinatorics of chord diagrams. We prove that contact elements are in bijective correspondence with comparable pairs of basis elements with respect to a certain partial order, and in a natural and explicit way. We also prove numerous results about the structure of contact elements and investigate various algebraic structures which arise. Our main theorem, describing how contact elements lie in sutured Floer homology, has a purely combinatorial interpretation, as a statement about chords on discs subject to a certain surgery and a single addition relation. The algebraic and combinatorial structures which naturally arise in this description have intrinsic contact-topological meaning. In particular, the QFT-type basis of sutured Floer homology, and its partial order, have a
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Lefrancois, M
2005-12-15
In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)
A first course in topos quantum theory
Energy Technology Data Exchange (ETDEWEB)
Flori, Cecilia [Perimeter Institute for Theoretical Studies, Waterloo, ON (Canada)
2013-06-01
Written by a leading researcher in the field. Concise course-tested textbook. Includes worked-out problems In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory's unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics - such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer - is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a ''neo-realist'' classical physics theory again.
Directory of Open Access Journals (Sweden)
Zhaosen Liu
2017-05-01
Full Text Available We use a recently developed quantum simulation approach to study the properties of a three-dimensional Ising model consisting of S = 1/2 quantum spins localized at the sites of a simple cubic lattice. We assume nearest-neighbor interaction between spins with an exchange interaction that can be either ferromagnetic or antiferromagnetic. It is found that the computational method quickly converges towards the expected equilibrium spin configurations. The resulting spontaneous magnetization curves corresponding to the two types of magnetic interactions under consideration were found to be almost identical to the ones obtained via quantum mean field theory at all temperatures. The derived total energies, total free energies, magnetic entropies and specific heats per mole of spins show no sizeable differences from known theoretical values. Furthermore, the results of the simulations for two different 3D Ising systems containing 4×4×4 and 20×20×20 spins localized at the sites of a simple cubic lattice were found to be almost identical to each other. This finding suggests that the self-consistent algorithm approach of the current simulation method allows one to obtain the physical bulk properties of a large magnetic system by relying on simulations of a much smaller spin system sample. Therefore, the method presently considered appears to be not only very accurate as gauged by comparison to mean field theory, but also able to greatly increase the speed of simulations.
Relativistic Quantum Information Theory
2007-11-20
Relativistic Quantum Information Theory Army Research Office Grant # DAAD -0301-0207 Christoph Adami November 16, 2007 1 Foreword The stated goal of the...the future will allow us to finish the work we started. A List of manuscripts produced under ARO grant # DAAD - 0301-0207 All these manuscripts
Höhn, Philipp Andres; Wever, Christopher S. P.
2017-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S 's state as O 's "catalog of knowledge" about S . From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C2N; (b) states evolve unitarily under the group PSU (2N) according to the von Neumann evolution equation; and (c) O 's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels previously unnoticed structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a "charge of quantum theory" and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in a companion paper (P. Höhn, arXiv:1412.8323).
The role of quantum discord in quantum information theory
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Streltsov, Alexander [ICFO - The Institute of Photonic Sciences, Castelldefels (Spain)
2014-07-01
Quantum correlations beyond entanglement - in particular represented by quantum discord - have become a major research field in the last few years. In this talk we report on the role of quantum discord in several fundamental tasks in quantum information theory. Starting with the role of quantum discord in the quantum measurement process, we also discuss its role in the tasks of information sharing and entanglement distribution. Finally, we also show the limits of these results and present possible ways to go beyond these limits.
Are Quantum Theory Questions Epistemic?
Directory of Open Access Journals (Sweden)
Viviana Yaccuzzi Polisena
2013-12-01
Full Text Available How to displace-move quantum theory [Ǭ] questions-problems to philosophy? Seeing the collapse of our society’s cultural-intellectual-morals, the philosophy of the 21st century has to contribute to the formation of new principles-formalisms: the big task of the contemporary philosophy ©] is to innovate, to transform the building of the knowledge! Which is the role of the contemporary philosopher? (Noam Chomsky. Building science so that it is more human, out of the scientific mercantilism so that it does not continue transgressing that which is most precious: the thought-life. The ideas that I propose demand a deep cultural-epistemiologicscientific-philosophical-ethical rethinking that goes from quantum entities up to life in society. The starting idea is «the quantum [Ǭ], the paradigm of the contemporary science ©]» (Bernard D’Espagnat. I propose to displace-move questions of the quantum theory [Ǭ]: spin, measure, layering to the field of philosophy (φ to build generic symbols. Can the contemporary episteme model the collapse of the ? For a philosopher, can understanding the importance and the behaviour of the spin bring something new to philosophy ? Can information of the states of the spin be used to observe in a holographic way the pattern energy-information contained in the quantum entities? Is quantum [Ǭ] physics mechanical?
Von Weizsäcker, Carl Friedrich
1988-01-01
1- presentation of quantum theory in present-day physics. 2- a flash-back on the history : from Planck to Copenhagen. 3- the Copenhagen interpretation. 4- reconstrucction of Abstract Quantum Theory. 5- recent interpretations. 6- the philosophy of the mind. 7- concrete quantum theory. 8- the non-locality. This second tape contains the debate following the talk of the professor.
Chen, Zhangjin; Liang, Yaqiu; Lin, C D
2010-06-25
Based on the full quantal recollision model and field-free electron impact ionization theory, we calculate the correlated momentum spectra of the two outgoing electrons in strong field nonsequential double ionization (NSDI) of helium to compare with recent experiments. By analyzing the relative strength of binary versus recoil collisions exhibited in the photoelectron spectra, we confirm that the observed fingerlike structure in the experiment is a consequence of the Coulomb interaction between the two emitted electrons. Our result supports the recollision mechanism of strong field NSDI at the most fundamental level.
KMS-like properties of local equilibrium states in quantum field theory
Gransee, Michael; Pinamonti, Nicola; Verch, Rainer
2017-07-01
A new condition, called ;Local KMS Condition;, characterizing states of a quantum field to which one can ascribe, at a given spacetime point, a temperature, is introduced in this article. It will be shown that the Local KMS Condition (LKMS condition) is equivalent to the Local Thermal Equilibrium (LTE) condition, proposed previously by Buchholz, Ojima and Roos, for states of the quantized scalar Klein-Gordon field that fulfill the analytic microlocal spectrum condition. Therefore, known examples of states fulfilling the LTE condition provide examples of states obeying the LKMS condition with a temperature distribution varying in space and time. The results extend to the generalized cases of mixed-temperature LKMS and LTE states. The LKMS condition therefore provides a promising generalization of the KMS condition, which characterizes global thermal equilibrium states with respect to an inertial time evolution, to states which are globally out of equilibrium but still possess a local temperature distribution.
12th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory
LL2014
2014-01-01
The bi-annual international conference “Loops and Legs in Quantum Field Theory” has been held at Weimar, Germany, from April 27 to May 02, 2014. It has been the 12th conference of this series, started in 1992. The main focus of the conference are precision calculations of multi- loop and multi-leg processes in elementary particle physics for processes at present and future high-energy facilities within and beyond the Standard Model. At present many physics questions studied deal with processes at the LHC and future facilities like the ILC. A growing number of contributions deals with important developments in the field of computational technologies and algorithmic methods, including large-scale computer algebra, efficient methods to compute large numbers of Feynman diagrams, analytic summation and integration methods of various kinds, new related function spaces, precise numerical methods and Monte Carlo simulations. The present conference has been attended by more than 110 participants from all over the ...
Huang, Yi-Ping; Hermele, Michael
Some pyrochlore oxides realize novel dipolar-octupolar (DO) doublets on the sites of the pyrochlore lattice of corner-sharing tetrahedra. With magnetic field along the (111) direction, such systems can approximately be described as decoupled layers of a S =1/2 XYZ model on Kagome planes, with perpendicular magnetic field. A recent quantum Monte Carlo study found a zero temperature disordered phase in this model, dubbed quantum kagome ice, and proposed that it is a type of Z2 quantum spin liquid (J. Carrasquilla, Z. Hao and R. G. Melko, Nat. Comm., 6, 7421). We will describe an effective theory for this putative Z2 spin liquid, and present results on its symmetry fractionalization and resulting properties that may be tested in future numerical simulations. the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
Quantum theory informational foundations and foils
Spekkens, Robert
2016-01-01
This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quant...
Energy Technology Data Exchange (ETDEWEB)
Zinn-Justin, J
2003-08-01
In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
Realization of Symmetry in the ERG Approach to Quantum Field Theory
Igarashi, Yuji; Itoh, Katsumi; Sonoda, Hidenori
We review the use of the exact renormalization group forrealization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sect. 2--4), we start with the perturbative construction of a renormalizable field theory as a solution of the exact renormalization group (ERG) differential equation. We show how to characterize renormalizability by an appropriate asymptotic behavior of the solution for a large momentum cutoff. Renormalized parameters are introduced to control the asymptotic behavior. In part II (sect. 5--9), we introduce two formalisms to incorporate symmetry: one by imposing the Ward-Takahashi identity, and the other by imposing the generalized Ward-Takahashi identity via sources that generate symmetry transformations. We apply the two formalisms to concrete models such as QED, YM theories, and the Wess-Zumino model in four dimensions, and the O(N) non-linear sigma model in two dimensions. We end this part with calculations of the abelian axial and chiral anomalies. In part III (sect. 10 and 11), we overview the Batalin-Vilkovisky formalism adapted to the Wilson action of a bare theory with a UV cutoff. We provide a few appendices to give details and extensions that can be omitted for the understanding of the main text. The last appendix is a quick summary for the reader's convenience.
Orthodontics in a quantum world III: electromagnetic field theory and oral parafunction.
James, Gavin
2008-01-01
The study of electromagnetic field theory and bioenergy has established that there is an extensive communication system throughout the body by way of a functional matrix. This enables the body to use the mouth to assist it during the expenditure of effort elsewhere in the body. A variety of oral behaviors can be identified as contributing to this. To some extent, these behaviors indicate where an imbalance is present in the body.
Effective field theory of an anomalous Hall metal from interband quantum fluctuations
Chua, Victor; Assawasunthonnet, Wathid; Fradkin, Eduardo
2017-07-01
We construct an effective field theory, a two-dimensional two-component metallic system described by a model with two Fermi surfaces ("pockets"). This model describes a translationally invariant metallic system with two types of fermions, each with its own Fermi surface, with forward scattering interactions. This model, in addition to the O (2 ) rotational invariance, has a U (1 )×U (1 ) symmetry of separate charge conservation for each Fermi surface. For sufficiently attractive interactions in the d -wave (quadrupolar) channel, this model has an interesting phase diagram that includes a spontaneously generated anomalous Hall metal phase. We derive the Landau-Ginzburg effective action of quadrupolar order parameter fields which enjoys an O (2 )×U (1 ) global symmetry associated to spatial isotropy and the internal U (1 ) relative phase symmetries, respectively. We show that the order parameter theory is dynamically local with a dynamical scaling of z =2 and perform a one-loop renormalization group analysis of the Landau-Ginzburg theory. The electronic liquid crystal phases that result from spontaneous symmetry breaking are studied and we show the presence of Landau damped Nambu-Goldstone modes at low momenta that is a signature of non-Fermi-liquid behavior. Electromagnetic linear response is also analyzed in both the normal and symmetry broken phases from the point of view of the order parameter theory. The nature of the coupling of electromagnetism to the order parameter fields in the normal phase is non-minimal and decidedly contains a precursor to the anomalous Hall response in the form of a order-parameter-dependent Chern-Simons term in the effective action.
Applications of Quantum Field Theory, From the Formal to the Phenomenological
Grabowska, Dorota
Much of the beautiful and complex phenomenology of the Standard Model can be traced back to the presence of chiral symmetries, both global and local, and nonperturbative phenomena. Without chiral symmetries (and the anomalous ways that they can be broken), there would be no flavor physics or CP violation. Without a strongly coupled sector, the richly intricate structure of the hadron spectrum would be lost. After introducing the Standard Model and some of its phenomenological aspects, as well as some of the tools that are used to explore its structure, I will focus on my contributions to several open problems in flavor physics, lattice field theory and astrophysics.
Colosi, Daniele; Dohse, Max
2017-04-01
We use the General Boundary Formulation (GBF) of Quantum Field Theory to compute the S-matrix for a general interacting scalar field in a wide class of curved spacetimes. As a by-product we obtain the general expression of the Feynman propagator for the scalar field, defined in the following three types of spacetime regions. First, there are the familiar interval regions (e.g. a time interval times all of space). Second, we consider the rod hypercylinder regions (all of time times a solid ball in space). Third, the tube hypercylinders (all of time times a solid shell in space) are related to interval regions, and result from removing a smaller rod from a concentric larger one. Using the Schrödinger representation for the quantum states combined with Feynman's path integral quantization, we obtain the S-matrix as the asymptotic limit of the GBF amplitude associated with finite interval, and rod regions. For interval regions, whose boundary consists of two Cauchy surfaces, the asymptotic GBF-amplitude becomes the standard S-matrix. Our work generalizes previous results (obtained in Minkowski, Rindler, de Sitter, and Anti de Sitter spacetimes) to a wide class of curved spacetimes.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Electric fields and quantum wormholes
Engelhardt, D.; Freivogel, B.; Iqbal, N.
2015-01-01
Electric fields can thread a classical Einstein-Rosen bridge. Maldacena and Susskind have recently suggested that in a theory of dynamical gravity the entanglement of ordinary perturbative quanta should be viewed as creating a quantum version of an Einstein-Rosen bridge between the particles, or a
Quantum Field Symbolic Analog Computation: Relativity Model
Manoharan, A. C.
2000-01-01
It is natural to consider a quantum system in the continuum limit of space-time configuration. Incorporating also, Einstein's special relativity, leads to the quantum theory of fields. Non-relativistic quantum mechanics and classical mechanics are special cases. By studying vacuum expectation values (Wightman functions W(n; z) where z denotes the set of n complex variables) of products of quantum field operators in a separable Hilbert space, one is led to computation of holomorphy domains for...
The Nonlinear Field Space Theory
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Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Directory of Open Access Journals (Sweden)
Jakub Mielczarek
2016-08-01
Full Text Available In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity, as well as in condensed matter physics (e.g. continuous spin chains, and can shed new light on the issue of divergences in quantum field theories.
What is really "quantum" in quantum theory?
Khrennikov, Andrei
2003-01-01
By analysing probabilistic foundations of quantum theory we understood that the so called quantum calculus of probabilities (including Born's rule) is not the main distinguishing feature of "quantum". This calculus is just a special variant of a contextual probabilistic calculus. In particular, we analysed the EPR-Bohm-Bell approach by using contextual probabilistic models (e.g., the frequency von Mises model). It is demonstrated that the EPR-Bohm-Bell consideration are not so much about "qua...
Holomorphic field realization of SH{sup c} and quantum geometry of quiver gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bourgine, Jean-Emile [INFN Bologna, Università di Bologna,Via Irnerio 46, 40126 Bologna (Italy); Matsuo, Yutaka [Department of Physics, The University of Tokyo,Hongo 7-3-1, Bunkyo-ku, Tokyo (Japan); Zhang, Hong [Department of Physics and Center for Quantum Spacetime (CQUeST),Sogang University,35 Baekbeom-ro, Mapo-gu, Seoul 04107 (Korea, Republic of)
2016-04-27
In the context of 4D/2D dualities, SH{sup c} algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N=2 supersymmetric gauge theories. In this paper, we rewrite the SH{sup c} algebra in terms of three holomorphic fields D{sub 0}(z), D{sub ±1}(z) with which the algebra and its representations are simplified. The instanton partition functions for arbitrary N=2 super Yang-Mills theories with A{sub n} and A{sub n}{sup (1)} type quiver diagrams are compactly expressed as a product of four building blocks, Gaiotto state, dilatation, flavor vertex operator and intertwiner which are written in terms of SH{sup c} and the orthogonal basis introduced by Alba, Fateev, Litvinov and Tarnopolskiy. These building blocks are characterized by new conditions which generalize the known ones on the Gaiotto state and the Carlsson-Okounkov vertex. Consistency conditions of the inner product give algebraic relations for the chiral ring generating functions defined by Nekrasov, Pestun and Shatashvili. In particular we show the polynomiality of the qq-characters which have been introduced as a deformation of the Yangian characters. These relations define a second quantization of the Seiberg-Witten geometry, and, accordingly, reduce to a Baxter TQ-equation in the Nekrasov-Shatashvili limit of the Omega-background.
Quantum gravity from theory to experimental search
Kiefer, Claus; Lämmerzahl, Claus
2003-01-01
The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.
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Pinto Neto, N.; Santini, E. Sergio [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: nelsonpn@lafex.cbpf.br; santini@lafex.cbpf.br
2000-07-01
In this work some characteristics of the Bohm-de Broglie interpretation in field theory. Interesting results for the field theory are found, such as the proof of the general consistency and the break of the relativistic invariance for individual processes. The methodology developed in this paper is useful as introduction for the study of quantum gravitation and cosmology in the Bohm-de Broglie interpretation.
Pejhan, Hamed; Rahbardehghan, Surena
2016-04-01
Respecting that any consistent quantum field theory in curved space-time must include black hole radiation, in this paper, we examine the Krein-Gupta-Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman-Gärding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy-momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field to vanish. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy-momentum tensor. On this basis, by evaluating the Casimir energy-momentum tensor for a conformally coupled massless scalar field in the vicinity of a nonrotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.
M theory as a holographic field theory
Hořava, Petr
1999-02-01
We suggest that M theory could be nonperturbatively equivalent to a local quantum field theory. More precisely, we present a ``renormalizable'' gauge theory in eleven dimensions, and show that it exhibits various properties expected of quantum M theory, most notably the holographic principle of 't Hooft and Susskind. The theory also satisfies Mach's principle: A macroscopically large space-time (and the inertia of low-energy excitations) is generated by a large number of ``partons'' in the microscopic theory. We argue that at low energies in large eleven dimensions, the theory should be effectively described by eleven-dimensional supergravity. This effective description breaks down at much lower energies than naively expected, precisely when the system saturates the Bekenstein bound on energy density. We show that the number of partons scales like the area of the surface surrounding the system, and discuss how this holographic reduction of degrees of freedom affects the cosmological constant problem. We propose the holographic field theory as a candidate for a covariant, nonperturbative formulation of quantum M theory.
Quantum theory of electroabsorption in semiconductor nanocrystals.
Tepliakov, Nikita V; Leonov, Mikhail Yu; Baranov, Alexander V; Fedorov, Anatoly V; Rukhlenko, Ivan D
2016-01-25
We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.
Directory of Open Access Journals (Sweden)
Gift S.
2009-01-01
Full Text Available In this paper, a new Quantum Theory of Magnetic Interaction is proposed. This is done under a relaxation of the requirement of covariance for Lorentz Boost Transformations. A modified form of local gauge invariance in which fermion field phase is allowed to vary with each space point but not each time point, leads to the introduction of a new compensatory field different from the electromagnetic field associated with the photon. This new field is coupled to the magnetic flux of the fermions and has quanta called magnatons, which are massless spin 1 particles. The associated equation of motion yields the Poisson equation for magnetostatic potentials. The magnatons mediate the magnetic interaction between magnetic dipoles including magnets and provide plausi- ble explanations for the Pauli exclusion principle, Chemical Reactivity and Chemical Bonds. This new interaction has been confirmed by numerical experiments. It estab- lishes magnetism as a force entirely separate from the electromagnetic interaction and converts all of classical magnetism into a quantum theory.
Pavlov, Y V
2001-01-01
One derived expressions for the vacuum mean values of energy-momentum tensor of the scalar field with arbitrary relation to curvature in N-dimensional quasi-euclidean space-time for vacuum. One generalized n-wave procedure for multidimensional spaces. One calculated all counter-members for N=5 and for a conformal scalar field in N=6, 7. One determined the geometric structure of three first counter-members for N-dimensional spaces. All subtractions in 4-dimensional space-time and 3 first subtractions in multidimensional spaces are shown to correspond to renormalization of constants of priming and gravitational Lagrangian
Introduction to the theory of quantum information processing
Bergou, János A
2013-01-01
Introduction to the Theory of Quantum Information Processing provides the material for a one-semester graduate level course on quantum information theory and quantum computing for students who have had a one-year graduate course in quantum mechanics. Many standard subjects are treated, such as density matrices, entanglement, quantum maps, quantum cryptography, and quantum codes. Also included are discussions of quantum machines and quantum walks. In addition, the book provides detailed treatments of several underlying fundamental principles of quantum theory, such as quantum measurements, the no-cloning and no-signaling theorems, and their consequences. Problems of various levels of difficulty supplement the text, with the most challenging problems bringing the reader to the forefront of active research. This book provides a compact introduction to the fascinating and rapidly evolving interdisciplinary field of quantum information theory, and it prepares the reader for doing active research in this area.
From classical to quantum fields
Baulieu, Laurent; Sénéor, Roland
2017-01-01
Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a re...
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
Quantum fields on the computer
1992-01-01
This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.
Quantum algorithms for number fields
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Haase, D.; Maier, H. [Universitaet Ulm, Fakultaet fuer Mathematik und Wirtschaftswissenschaften, Helmholtzstrasse 18, 89069 Ulm (Germany)
2006-08-23
This is a survey of recent results on quantum algorithms for the computation of invariants of number fields, namely the class number and the regulator. Most known classical algorithms for the computation of these values are of subexponential complexity and depend on the truth of a still unproven hypothesis of analytic number theory. We use an important number theoretic concept, Minkowski's Geometry of Numbers, to visualize these invariants, and describe the quantum algorithms developed by Hallgren, Schmidt and Vollmer which compute these invariants using a polynomial number of steps. Computational techniques in number fields, which are necessary to justify the classical part of these quantum algorithms, are the focus of the research of our project group, and are explained in detail. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
The Fuzzy analogy of chiral diffeomorphisms in higher dimensional quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Fassarella, Lucio; Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: fassarel@cbpf.br; schroer@cbpf.br
2001-06-01
Our observation that the chiral diffeomorphisms allow an interpretation as modular groups of local operator algebras in the sense of Tomita and takesaki allows us to conclude that the higher deimensional generalizations are certain infinite dimensional groups which act in a 'fuzzy' way on the operator algebras of local quantum physics. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. The use of an appropriately defined isomorphism reprocesses these fuzzy actions into partially geometric actions on the holographic image and in this way tightens the relation with chiral structures and makes recent attempts to explain the required universal structure of a would be quantum Bekenstein law in terms of Virasoro algebra structures more palatable. (author)
2D quantum field theories away from criticality: Finite-size scaling, the C-theorem and the S-matrix
Energy Technology Data Exchange (ETDEWEB)
Mavromatos, N.E. (Oxford Univ. (UK). Dept. of Theoretical Physics Hertford Coll., Oxford (UK)); Miramontes, J.L.; Sanchez de Santos, J.M. (Universidad de Santiago de Compostela (Spain). Dept. de Particulas Elementales)
1990-08-01
Issues concerning the behavior of renormalizable 2D quantum field theories away from criticality are addressed. Connection of Zamolodchikov's c-function with the generating functional of connected correlators is established using a finite-size scaling approach. (orig.).
Topological quantum field theory and the Nielsen-Thurston classification of M(0,4)
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Masbaum, G.; Ueno, K.
2006-01-01
We show that the Nielsen–Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum $SU(n)$ representations, for any fixed $n\\geq 2$. In the Pseudo–Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) $SU......)$-TQFT representation matrices. It follows that at big enough levels, Pseudo–Anosov mapping classes are represented by matrices of infinite order....
Robert R. Wilson Prize II: A Quantum Field Theory Approach to Intrabeam Scattering
Bjorken, James
2017-01-01
My involvement in the intrabeam scattering problem was very brief, from the autumn of 1981 to the summer of 1982. It occurred during my tenure at Fermilab. I entered the subject as an amateur in accelerator theory. But my experience in elementary-particle theory turned out to be of help in advancing the subject.
Problem of the Landau Poles in Quantum Field Theory: from N. N. Bogolyubov to the Present Day
Jafarov, R. G.; Agham-Alieva, L. A.; Agha-Kishieva, P. É.; Rahim-zade, S. G.; Mamedova, S. N.; Mutallimov, M. M.
2017-03-01
A review of problems associated with the unphysical Landau pole in propagators of quantum particles is given. Approaches to eliminating this pole within the framework of electrodynamics and effective theories of strongly interacting particles are investigated. The asymptotic behavior at large momenta in the scalar theory ϕ4 in the two-particle (bubble) approximation is investigated. To formulate a calculational model in the two-particle approximation, we use an iterative scheme for solving the Schwinger-Dyson equation in the formalism of a bilocal field source. The main problem is to develop a recipe for numerical analysis of the solutions of the obtained nonlinear equation for the amplitude at small interaction distances (large values of the momentum) for different values of the constant. The nontrivial behavior of the amplitude in the deeply inelastic region of momenta is determined. The positions of the unphysical poles (the Landau poles) in the expression for the amplitude in the deeply inelastic region of momenta are identified.
Self-mass of vector bosons in gravity-modified quantum field theories
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Poelt, P. (Technische Univ., Graz (Austria). Inst. fuer Theoretische Physik)
1985-01-01
The self-mass of the W-boson is calculated using a gravitational modified Weinberg-Salam theory with an anomalous magnetic moment assumed to be variable. The self-mass is shown to be finite with Gsub(N)sup(-1/2) (Gsub(N) Newton's gravitational constant) as the cutoff parameter. But only certain values of the anomalous magnetic moment yield a correct order of magnitude. Lowest order of perturbation theory gives complex solutions for these magnetic moments. Nevertheless, additional terms of higher perturbation theory will modify the equation for the magnetic moment and possibly lead to the definite magnetic moment of the W-boson of the non-modified Weinberg-Salam theory.
Quantum theory a mathematical approach
Bongaarts, Peter
2015-01-01
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
The quantum theory of measurement
Busch, Paul; Mittelstaedt, Peter
1996-01-01
The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables and unsharp pointers.
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Boundary state in an integrable quantum field theory out of equilibrium
Energy Technology Data Exchange (ETDEWEB)
Sotiriadis, Spyros [Department of Physics, University of Pisa (Italy); INFN, Pisa section (Italy); Takacs, Gabor [Department of Theoretical Physics, Budapest University of Technology and Economics (Hungary); MTA-BME “Momentum” Statistical Field Theory Research Group (Hungary); Mussardo, Giuseppe [SISSA and INFN, Trieste (Italy); The Abdus Salam ICTP, Trieste (Italy)
2014-06-27
We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitations. We argue that the large energy profile of the involved excitations can be relevant for the late time behaviour of the system and common regularization schemes are unreliable. We therefore proceed in determining the initial state by first principles expanding it in a systematic and controllable fashion on the basis of the asymptotic states. Our results show that, for the special limit of pre-quench parameters we consider, it assumes a squeezed state form that has been shown to evolve so as to exhibit the equilibrium behaviour predicted by the Generalized Gibbs Ensemble.
Pressley, Andrew
2002-02-01
To take stock and to discuss the most fruitful directions for future research, many of the world's leading figures met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.
Simplicial gauge theory and quantum gauge theory simulation
Energy Technology Data Exchange (ETDEWEB)
Halvorsen, Tore Gunnar, E-mail: toregha@gmail.com [Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim (Norway); Sorensen, Torquil Macdonald, E-mail: t.m.sorensen@matnat.uio.no [Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo (Norway)
2012-01-01
We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of {beta}.
The XXth International Workshop High Energy Physics and Quantum Field Theory
The Workshop continues a series of workshops started by the Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State University (SINP MSU) in 1985 and conceived with the purpose of presenting topics of current interest and providing a stimulating environment for scientific discussion on new developments in theoretical and experimental high energy physics and physical programs for future colliders. Traditionally the list of workshop attendees includes a great number of active young scientists and students from Russia and other countries. This year Workshop is organized jointly by the SINP MSU and the Southern Federal University (SFedU) and will take place in the holiday hotel "Luchezarniy" (Effulgent) situated on the Black Sea shore in a picturesque natural park in the suburb of the largest Russian resort city Sochi - the host city of the XXII Olympic Winter Games to be held in 2014. The main topics to be covered are: Experimental results from the LHC. Tevatron summary: the status of the Standard Model and the boundaries on BSM physics. Future physics at Linear Colliders and super B-factories. Extensions of the Standard Model and their phenomenological consequences at the LHC and Linear Colliders: SUSY extensions of the Standard Model; particle interactions in space-time with extra dimensions; strings, quantum groups and new ideas from modern algebra and geometry. Higher order corrections and resummations for collider phenomenology. Automatic calculations of Feynman diagrams and Monte Carlo simulations. LHC/LC and astroparticle/cosmology connections. Modern nuclear physics and relativistic nucleous-nucleous collisions.
Quantum theory a wide spectrum
Manoukian, E B
2006-01-01
Suitable for instructors and graduate students in Physics, and researchers and professional scientists in Theoretical Physics, this textbook focuses on Quantum Theory. It includes traditional topics and contains numerous problems some of which are challenging enough for research
Elementary Concepts of Quantum Theory
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik
2010-02-15
After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge Andre Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to draw attention to the relevance of what at the time of Swieca was called 'the Schwinger Higgs screening mechanism'. which, together with recent ideas which generalize the concept of gauge theories, have all the ingredients to revolutionize the issue of gauge theories and the standard model. (author)
Energy Technology Data Exchange (ETDEWEB)
Fritzsch, Harald [Muenchen Univ. (Germany). Physik Dept.
2015-07-01
Do we already know the ''theory for all'' or are we still far away from it? Does at highest energies really a ''Grand Unification'' of all fundamental forces exist? And which role do play the string theory and the Higgs boson? Harald Fritzsch takes the reader along with a mathematical journey through the world of quantum field theory and presents so a large survey about the most actual status of modern theoretical physics.
Energy Technology Data Exchange (ETDEWEB)
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
Razavy, Mohsen
2014-01-01
In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and ...
Quantum theory, groups and representations an introduction
Woit, Peter
2017-01-01
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific ...
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness. Copyright © 2013 Cognitive Science Society, Inc.
Lectures on matrix field theory
Ydri, Badis
2017-01-01
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.
Energy Technology Data Exchange (ETDEWEB)
Maxfield, Travis [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States); Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Sethi, Savdeep [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States)
2016-11-28
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
Hoffman, Kenneth
2007-01-01
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover seq
2014-01-01
Wolfgang Pauli referred to him as 'my discovery', Robert Oppenheimer described him as 'one of the most gifted theorists' and Niels Bohr found him enormously stimulating. Who was the man in question, Gunnar Källén (1926-1968)? His appearance in the physics sky was like a shooting star. His contributions to the scientific debate caused excitement among young and old. Similar to his friend and mentor, Wolfgang Pauli, he demanded honesty and rigour in physics - a distinct dividing line between fact and speculation. In his obituary, Arthur S. Wightman would write: "Gunnar Källén was a proud continuer of the tradition in quantum field theory established by Wolfgang Pauli. His papers on quantum electrodynamics in the period 1950-1954 carried the non-perturbative approach to quantum electrodynamics forward to a point beyond which very little essential progress has been made up to the present day. At the time I was trying ...
Analytic aspects of quantum fields
Bytsenko, A A; Elizalde, E; Moretti, V; Zerbini, S
2003-01-01
One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist. Contents: Survey of Pa
Lee, Kyu Won; Lee, Cheol Eui
2015-12-01
We have investigated ABA-stacked trilayer graphene under a perpendicular electric field by using the density functional theory (DFT) calculations, which may contribute to the resolution of the discrepancies between experimental and theoretical results on the electric-field-induced band gap and topological phase transition. We found that the electric field opens a band gap at a low field and closes the gap at a high field, supporting one of the experimental results. While the seven electric-field-induced Dirac cones with mass gaps predicted in recent tight-binding (TB) models are confirmed, our DFT calculations demonstrate a phase transition from a quantum valley Hall insulator to a semimetal, contrasting to the TB model prediction of a topological phase transition between topologically nontrivial insulators at a high electric field.
Relativistic quantum mechanics an introduction to relativistic quantum fields
Maiani, Luciano
2016-01-01
Written by two of the world's leading experts on particle physics and the standard model - including an award-winning former Director General of CERN - this textbook provides a completely up-to-date account of relativistic quantum mechanics and quantum field theory. It describes the formal and phenomenological aspects of the standard model of particle physics, and is suitable for advanced undergraduate and graduate students studying both theoretical and experimental physics.
Two Quantum Effects In The Theory Of Gravitation
Robinson, S P
2005-01-01
We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an effective quantum field theory will be examined. The primary result will be the calculation of the first-order quantum gravity corrections to the β functions of arbitrary Yang-Mills theories. These corrections will effect the high-energy phenomenology of such theories, including the details of coupling constant unification. Following this, we will address the question of how to form effective quantum field theories in classical gravitational backgrounds. We follow the prescription that effective theories should provide a description of experimentally accessible degrees of freedom with all other degrees of freedom integrated out of the theory. We will show that this prescription appears to fail for a scalar field in a black hole background because of an anomaly generated in general cov...
Holography, Quantum Geometry, and Quantum Information Theory
Directory of Open Access Journals (Sweden)
P. A. Zizzi
2000-03-01
Full Text Available Abstract: We interpret the Holographic Conjecture in terms of quantum bits (qubits. N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labelled by the spin-Ã‚Â½ representation of SU(2, which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set and we get a quantum history. A (bosonic Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.
Non-Euclidean Geometry and Gravitation
Directory of Open Access Journals (Sweden)
Stavroulakis N.
2006-04-01
Full Text Available A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the non-Euclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical notion.
Causality Constraints in Conformal Field Theory
CERN. Geneva
2015-01-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinni...
Quantum kinetic theory of the chiral anomaly
Sekine, Akihiko; Culcer, Dimitrie; MacDonald, Allan H.
2017-12-01
We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field-induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wave-packet dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wave-packet dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.
Logarithmic conformal field theory
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Interpreting quantum theory a therapeutic approach
Friederich, S
2014-01-01
Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.
Quantum theory from first principles an informational approach
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-01-01
Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. The book is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 7. The Story of Quantum Theory. Abhijit Saha. Book Review Volume 9 Issue 7 July ... Abhijit Saha1. IIA, Bangalore 560 034, India (till Dec. 28,2004), Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile (January-July 2005).
The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.
Plotnitsky, Arkady
2016-05-28
Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT. © 2016 The Author(s).
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Quantum correlations beyond entanglement and their role in quantum information theory
Streltsov, Alexander
2015-01-01
Quantum correlations are not restricted to the well known entanglement investigated in Bell-type experiments. Other forms of correlations, for example quantum discord, have recently been shown to play an important role in several aspects of quantum information theory. First experiments also support these findings. This book is an introduction into this up-and-coming research field and its likely impact on quantum technology. After giving a general introduction to the concept of quantum correlations and their role in quantum information theory, the author describes a number of pertinent results and their implications.
Interpreting Quantum Theory : A Therapeutic Approach
Friederich, Simon
2014-01-01
Debates about the foundations of quantum theory usually circle around two main challenges: the so-called 'measurement problem' and a claimed tension between quantum theory and relativity theory that arises from the phenomena labelled 'quantum non-locality'. This work explores the possibility of a
Holographic applications of logarithmic conformal field theories
Grumiller, D.; Riedler, W.; Rosseel, J.; Zojer, T.
2013-01-01
We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in anti-de Sitter space and logarithmic conformal field theories in
Schroer, Bert
2009-01-01
The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive "outside-inwards approach" in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR, where dR is the thickness of a light sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of...
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik
2010-02-15
It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Born localization in QM (which in the relativistic context changes its name to Newton- Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. The present division into two semi-autonomous essays is the result of a partition and extension of an originally one-part manuscript. (author)
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Freie Univ. Berlin (Germany). Institut fuer Theoretische Physik
2010-07-01
It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Born-localization in QM (which in the relativistic context changes its name to Newton-Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. The present division into two semi-autonomous essays is the result of a partition and extension of an originally one-part manuscript. (author)
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik
2010-02-15
The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive 'outside-inwards approach' in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi-Metzner-Sachs group. This essay is the second part of a partitioned longer paper. (author)
Nonlocal continuum field theories
2002-01-01
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...
Superspace conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-07-15
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Field theories of condensed matter physics
Fradkin, Eduardo
2013-01-01
Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)
2016-06-06
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
Baden Fuller, A J
2014-01-01
Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation
A theory of quantum gravity based on quantum computation
Lloyd, Seth
2005-01-01
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of space-time is a construct, derived from the underlying quantum information processing. The computation gives rise to a superposition of four-dimensional spacetimes, each of which obeys the Einstein-Regge equations. The theory makes explicit predictions for t...
Gauge field theories an introduction with applications
Guidry, Mike
1991-01-01
Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises
A second course in topos quantum theory
Flori, Cecilia
2018-01-01
This advanced course, a sequel to the first volume of this lecture series on topos quantum theory, delves deeper into the theory, addressing further technical aspects and recent advances. These include, but are not limited to, the development of physical quantities and self-adjoint operators; insights into the quantization process; the description of an alternative, covariant version of topos quantum theory; and last but not least, the development of a new concept of spacetime. The book builds on the concepts introduced in the first volume (published as Lect. Notes Phys. 868), which presents the main building blocks of the theory and how it could provide solutions to interpretational problems in quantum theory, such as: What are the main conceptual issues in quantum theory? And how can these issues be solved within a new theoretical framework of quantum theory? These two volumes together provide a complete, basic course on topos quantum theory, offering a set of mathematical tools to readers interested in tac...
General relativistic quantum theories Foundations. Expanding Universes
Parmeggiani, Claudio
2015-07-01
Here the space-time is represented by the usual, four-dimensional manifold and at every space-time point is assigned an infinite-dimensional Hilbert space, seat of a (local) quantum description: states, probabilities and expectations. On the space-time manifold is assigned a metric tensor and it is assumed that the quantum fields commutations relations do not only depend on the metric tensor but also on its Ricci tensor: this is a fundamental postulate. This assumption has many relevant consequences: the theory is regularized; the commutators and the propagators are well defined functions and, applying the theory to electroweak interactions, we can obtain a finite and discrete specter of leptons masses.
Directory of Open Access Journals (Sweden)
Alejandro Morales-Bayuelo
2014-01-01
Full Text Available A theoretical study on the molecular polarization of thiophene and furan under the action of an electric field using Local Quantum Similarity Indexes (LQSI was performed. This model is based on Hirshfeld partitioning of electron density within the framework of Density Functional Theory (DFT. Six local similarity indexes were used: overlap, overlap-interaction, coulomb, coulomb-interaction, Euclidian distances of overlap, and Euclidean distances of coulomb. In addition Topo-Geometrical Superposition Algorithm (TGSA was used as a method of alignment. This method provides a straightforward procedure to solve the problem of molecular relative orientation. It provides a tool to evaluate molecular quantum similarity, enabling the study of structural systems, which differ in only one atom such as thiophene and furan (point group C2v and cyclopentadienyl molecule (point group D5h. Additionally, this model can contribute to the interpretation of chemical bonds, and molecular interactions in the framework of the solvent effect theory.
The Quantum Mechanics Solver How to Apply Quantum Theory to Modern Physics
Basdevant, Jean-Louis
2006-01-01
The Quantum Mechanics Solver grew from topics which are part of the final examination in quantum theory at the Ecole Polytechnique at Palaiseau near Paris, France. The aim of the text is to guide the student towards applying quantum mechanics to research problems in fields such as atomic and molecular physics, condensed matter physics, and laser physics. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills in this field.
Introduction to the quantum theory
Park, David
2005-01-01
More than a chance to gain new insights into physics, this book offers students the opportunity to look at what they already know about the subject in an improved way. Geared toward upper-level undergraduates and graduate students, this self-contained first course in quantum mechanics consists of two parts: the first covers basic theory, and the second part presents selected applications. Numerous problems of varying difficulty examine not only the steps of the proofs but also related ideas.Starting with an introduction that ventures beyond classical physics, the first part examines the physic
A first course in topos quantum theory
Flori, Cecilia
2013-01-01
In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility o...
Interpretting Information Based on Quantum Theory of Physics (Quantum Theory of Information)
Mitra pashootanizadeh; Mortaza kokabi
2014-01-01
There are different theories on information as Shannon's Information or Communication Theory, Semantic Theory of Information, Cybernetics Theory, Quantum Theory of Information and Quantum Information Theory, each one viewing information from a different point. In this paper researchers used the foundamental concepts of quantum physics such as Wave/Particle duality, Complementarity, Uncertainty principle, Schrödinger's cat & so on to explain the nature of information and i...
Energy Technology Data Exchange (ETDEWEB)
Hajj, G.A.
1988-01-01
The Gaussian effective potential (GEP), a non-perturbative approach to study quantum field theory, is applied to scalar and scalar-fermion models. We study the scalar {phi}{sup 6} field coupled to fermions through g{sub B}{phi}{psi}{psi} or g{sub B}{phi}{sup 2}{psi}{psi} in 2 and 3 space-time dimensions. In addition, we derive the finite temperature (T > 0) GEP from first principles and apply it to study these models at T > 0. Also the Autonomous {lambda}{phi}{sup 4}, coupled to fermions through a Yukawa term (g{sub B}{phi}{psi}{psi}), is examined in 4 dimensions at T > 0. In all these models, in order to obtain stable theories, it is found that g{sub B} must vanish as 1/log(M{sub uv}), 1/M{sub uv} or 1/M{sub uv}{sup 2} in 2, 3 or 4 dimensions respectively, M{sub uv} being an ultraviolet cutoff which is sent to infinity. The contribution of fermions to the GEP, however, is nonvanishing. It is also found that for the class of theories discussed, symmetry, if broken, is restored above a critical temperature. The coupling constant parameter space for each model is studied carefully, and regions where symmetry breaking occurs are determined both at zero and finite temperature.
Energy Technology Data Exchange (ETDEWEB)
Ranade, Kedar S.
2009-02-04
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
Diffusion, quantum theory, and radically elementary mathematics (MN-47)
Faris, William G
2014-01-01
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Mathematical Techniques for Quantum Communication Theory
Fuchs, Christopher A.; Caves, Carlton M.
1996-01-01
We present mathematical techniques for addressing two closely related questions in quantum communication theory. In particular, we give a statistically motivated derivation of the Bures-Uhlmann measure of distinguishability for density operators, and we present a simplified proof of the Holevo upper bound to the mutual information of quantum communication channels. Both derivations give rise to novel quantum measurements.
Intermediate spectral theory and quantum dynamics
de Oliveira, Cesar R
2008-01-01
The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. The book places emphasis on the symbiotic relationship of these two domains by (1) presenting the basic mathematics of nonrelativistic quantum mechanics of one particle, i.e., developing the spectral theory of self-adjoint operators in infinite-dimensional Hilbert spaces from the beginning, and (2) giving an overview of many of the basic functional aspects of quantum theory, from its physical principles to the mathematical models. The book is intended for graduate (or advanced undergraduate) students and researchers interested in mathematical physics. It starts with linear operator theory, spectral questions and self-...
Einstein's strugges with quantum theory a reappraisal
Home, Dipankar
2007-01-01
Einstein’s Struggles with Quantum Theory: A Reappraisal by Dipankar Home and Andrew Whitaker provides a detailed account of Albert Einstein’s thinking in regard to quantum physics. Until recently, most of Einstein’s views on quantum physics were dismissed and even ridiculed; some critics even suggested that Einstein was not able to grasp the complexities of the formalism of quantum theory and subtleties of the standard interpretation of this theory known as the Copenhagen interpretation put forward by Niels Bohr and his colleagues. But was that true? Modern scholarship argues otherwise, insist Drs. Home and Whitaker, who painstakingly explain the questions Einstein raised as well as offer a detailed discussion of Einstein’s position and major contributions to quantum theory, connecting them with contemporary studies on fundamental aspects of this theory. This unique book presents a mathematical as well as a non-mathematical route through the theories, controversies, and investigations, making the disc...
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, Alexander S
2011-01-01
This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation re
The Quantum Theory of Magnetism
Majlis, Norberto
2000-01-01
This book is intended as a basic text for a two-term graduate course for physicists, engineers and chemists with a background in quantum and statistical mechanics. What sets it apart from other publications on the subject is its extensive use of Greenâ€™s function techniques and its detailed discussion of the application of the mean-field approximation and dipoleâ€"dipole interactions in one, two and three dimensions. A chapter each has been devoted to low-dimensional systems, surface magnetism and layered systems. A total of 60 exercises have also been included.
Quantum entanglement: theory and applications
Energy Technology Data Exchange (ETDEWEB)
Schuch, N.
2007-10-10
This thesis deals with various questions concerning the quantification, the creation, and the application of quantum entanglement. Entanglement arises due to the restriction to local operations and classical communication. We investigate how the notion of entanglement changes if additional restrictions in form of a superselection rule are imposed and show that they give rise to a new resource. We characterize this resource and demonstrate that it can be used to overcome the restrictions, very much as entanglement can overcome the restriction to local operations by teleportation. We next turn towards the optimal generation of resources. We show how squeezing can be generated as efficiently as possible from noisy squeezing operations supplemented by noiseless passive operations, and discuss the implications of this result to the optimal generation of entanglement. The difficulty in describing the behaviour of correlated quantum many-body systems is ultimately due to the complicated entanglement structure of multipartite states. Using quantum information techniques, we investigate the ground state properties of lattices of harmonic oscillators. We derive an exponential decay of correlations for gapped systems, compute the dependence of correlation length and gap, and investigate the notion of criticality by relating a vanishing energy gap to an algebraic decay of correlations. Recently, ideas from entanglement theory have been applied to the description of many-body systems. Matrix Product States (MPS), which have a particularly simple interpretation from the point of quantum information, perform extremely well in approximating the ground states of local Hamiltonians. It is generally believed that this is due to the fact that both ground states and MPS obey an entropic area law. We clarify the relation between entropy scaling laws and approximability by MPS, and in particular find that an area law does not necessarily imply approximability. Using the quantum
Whiteheadian process and quantum theory
Energy Technology Data Exchange (ETDEWEB)
Stapp, H.
1998-08-01
There are deep similarities between Whitehead's idea of the process by which nature unfolds and the ideas of quantum theory. Whitehead says that the world is made of ''actual occasions'', each of which arises from potentialities created by prior actual occasions. These actual occasions are happenings modeled on experiential events, each of which comes into being and then perishes, only to be replaced by a successor. It is these experience-like happenings that are the basic realities of nature, according to Whitehead, not the persisting physical particles that Newtonian physics took be the basic entities. Similarly, Heisenberg says that what is really happening in a quantum process is the emergence of an actual from potentialities created by prior actualities. In the orthodox Copenhagen interpretation of quantum theory the actual things to which the theory refer are increments in ''our knowledge''. These increments are experiential events. The particles of classical physics lose their fundamental status: they dissolve into diffuse clouds of possibilities. At each stage of the unfolding of nature the complete cloud of possibilities acts like the potentiality for the occurrence of a next increment in knowledge, whose occurrence can radically change the cloud of possibilities/potentialities for the still-later increments in knowledge. The fundamental difference between these ideas about nature and the classical ideas that reigned from the time of Newton until this century concerns the status of the experiential aspects of nature. These are things such as thoughts, ideas, feelings, and sensations. They are distinguished from the physical aspects of nature, which are described in terms of quantities explicitly located in tiny regions of space and time. According to the ideas of classical physics the physical world is made up exclusively of things of this latter type, and the unfolding of the physical world is determined by
Field theory a path integral approach
Das, Ashok
2006-01-01
This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.
Continuous point symmetries in Group Field Theories
Kegeles, Alexander
2016-01-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equation of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity. We provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them, and apply it to several GFT models of interest to current research.
Н(1) Gauge theory as quantum hydrodynamics
Indian Academy of Sciences (India)
January 2004 physics pp. 101-114. Н(1) Gauge theory as quantum hydrodynamics. GIRIsH s sETLUR ... there is work by Ceperley [4] using quantum Monte Carlo. The main point of this article is to highlight the ..... Fermi liquid theory break down in two or three dimensions?' In two dimensions, for the interaction νХ = const.
Eringen, A Cemal
1999-01-01
Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balanc...
Quantum theory of acoustoelectric interaction
DEFF Research Database (Denmark)
Mosekilde, Erik
1974-01-01
term, significant in the classical-collision-dominated regime only, the dielectric response function and the acoustic gain factor for a piezoelectrically active sound wave are obtained for the quantum and semiclassical-microscopic regimes. The manner in which the theory can be extended to the collision......-dominated regime is discussed. For a collision-free electron gas, the requirements of energy and momentum conservation in individual electron-phonon interactions lead to a cutoff in the acoustoelectric coupling when the acoustic wave number exceeds the characteristic electron wave number. The broadening...... of this cutoff due to collisions is investigated and compared with thermal broadening. A number of useful approximations for the acoustic gain factor are derived....
Measurement theory in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Okamura, Kazuya, E-mail: okamura@math.cm.is.nagoya-u.ac.jp; Ozawa, Masanao, E-mail: ozawa@is.nagoya-u.ac.jp [Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601 (Japan)
2016-01-15
In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated by CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.
Electromagnetism in Euclidean four space: A discussion between God and the Devil
Heras, José A.
1994-10-01
In this paper we reexamine the known argument by which Maxwell's equations are ``derived'' from the gauge invariance of quantum mechanics, or alternatively, from the gauge invariance of classical mechanics. We point out that this argument is ambiguous in the sense that it may lead us equally to another theory different from that of Maxwell, namely, an electromagnetic theory in Euclidean four space. We attempt to enliven our discussion by presenting it as a dialogue between God and the Devil.
Quantum Interference and Coherence Theory and Experiments
Ficek, Zbigniew; Rhodes, William T; Asakura, Toshimitsu; Brenner, Karl-Heinz; Hänsch, Theodor W; Kamiya, Takeshi; Krausz, Ferenc; Monemar, Bo; Venghaus, Herbert; Weber, Horst; Weinfurter, Harald
2005-01-01
For the first time, this book assembles in a single volume accounts of many phenomena involving quantum interference in optical fields and atomic systems. It provides detailed theoretical treatments and experimental analyses of such phenomena as quantum erasure, quantum lithography, multi-atom entanglement, quantum beats, control of decoherence, phase control of quantum interference, coherent population trapping, electromagnetically induced transparency and absorption, lasing without inversion, subluminal and superluminal light propagation, storage of photons, quantum interference in phase space, interference and diffraction of cold atoms, and interference between Bose-Einstein condensates. This book fills a gap in the literature and will be useful to both experimentalists and theoreticians.
CERN. Geneva; CERN. Geneva
2001-01-01
Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Energy Technology Data Exchange (ETDEWEB)
Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Gravitational descendants in symplectic field theory
Fabert, O.
2011-01-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic
Beyond Quantum Fields: A Classical Fields Approach to QED
Directory of Open Access Journals (Sweden)
Chafin C.
2015-07-01
Full Text Available A classical field theory is introduced that is defined on a tower of dimensionally in- creasing spaces and is argued to be equivalent to QED. The domain of dependence is discussed to show how an equal times picture of the many coordinate space gives QED results as part of a well posed initial value formalism. Identical particle symmetries are not, a priori, required but when introduced are clearly propagated. This construc- tion uses only classical fields to provide some explanation for why quantum fields and canonical commutation results have been successful. Some old and essential questions regarding causality of propagators are resolved. The problem of resummation, gener- ally forbidden for conditionally convergent series, is dis cussed from the standpoint of particular truncations of the infinite tower of functions an d a two step adiabatic turn on for scattering. As a result of this approach it is shown that the photon inherits its quantization ~ ω from the free lagrangian of the Dirac electrons despite the fact that the free electromagnetic lagrangian has no ~ in it. This provides a possible explanation for the canonical commutation relations for quantum operators , [ ˆ P , ˆ Q ] = i ~ , without ever needing to invoke such a quantum postulate. The form of the equal times conservation laws in this many particle field theory suggests a simplification of the radiation reaction process for fields that allows QED to arise from a sum of path integrals in the various particle time coordinates. A novel method of unifying this theory with gravity, but that has no obvious quantum field theoretic computational scheme , is introduced.
Picturing quantum processes a first course in quantum theory and diagrammatic reasoning
Coecke, Bob
2017-01-01
The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying proc...
Emergent "Quantum" Theory in Complex Adaptive Systems.
Minic, Djordje; Pajevic, Sinisa
2016-04-30
Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.
Frames, designs, and spherical codes in quantum information theory
Renes, Joseph M.
Frame theory offers a lens through which to view a large portion of quantum information theory, providing an organizational principle to those topics in its purview. In this thesis, I cut a trail from foundational questions to practical applications, from the origin of the quantum probability rule to quantum cryptography, by way of a standard quantum measurement helpful in quantum tomography and representation of quantum theory. Before embarking, preparations are undertaken by outlining the relevant aspects of frame theory, particularly the characterization of generalized orthonormal bases in terms of physical quantum measurements, as well as several aesthetically appealing families of measurements, each possessing a high degree of symmetry. Much more than just elegant, though, these quantum measurements are found to be useful in many aspects of quantum information theory. I first consider the foundational question of justifying the quantum probability rule, showing that putting a probability valuation on generalized quantum measurements leads directly to the Born rule. Moreover, for qubits, the case neglected in the traditional formulation of Gleason's theorem, a symmetric three-outcome measurement called the trine is sufficient to impel the desired form. Keeping with foundational questions, I then turn to the problem of establishing a symmetric measurement capable of effortlessly rendering quantum theory in terms of classical probability theory. Numerical results provide an almost utterly convincing amount of evidence for this, justifying the subsequent study of its use in quantum tomography and detailed account of the properties of the reduction to probabilistic terms. Saving perhaps the most exciting topic for last, I make use of these aesthetic ensembles in the applied field of quantum cryptography. A large class of streamlined key distribution protocols may be cut from the cloth of these ensembles, and their symmetry affords them improved tolerance to
Quantum Field of Nonstationary Polaron
Khrustalev, O. A.; Tchitchikina, M. V.; Spirina, E. Yu.
2001-04-01
Polaron problem is considered. Bogoliubov group variables for the space-time translations group are defined. The scheme of secondary quantization for the scalar field interacting with charged quantum field is proposed. Scalar field is assumes to have nonzero classical component. Polaron is treated as a result of interaction of charged particle and neutral field classical component. The system state space is constructed. Expressions for integrals of motion in zero-point order with respect to inverted powers of coupling constant are given as a derivatives with respect to symmetry group generators.
Positive Cosmological Constant and Quantum Theory
Directory of Open Access Journals (Sweden)
Felix M. Lev
2010-11-01
Full Text Available We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli.
Random-matrix theory of quantum transport
Energy Technology Data Exchange (ETDEWEB)
Beenakker, C.W. [Instituut-Lorentz, University of Leiden, 2300 RA Leiden, (The Netherlands)
1997-07-01
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson{close_quote}s circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear {sigma} model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. {copyright} {ital 1997} {ital The American Physical Society}
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014 that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory” is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of PT-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Entanglement in non-Hermitian quantum theory
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 73; Issue 3. Entanglement in non-Hermitian quantum theory. Arun K Pati. Volume 73 Issue 3 ... Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product ...
"Scars" connect classical and quantum theory
Monteiro, T
1990-01-01
Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).
Teaching Quantum Theory in the Introductory Course.
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Molecular quantum dynamics from theory to applications
Gatti, Fabien
2014-01-01
Emphasizing fundamental educational concepts, this book offers an accessible introduction that covers eigenstates, wave packets, quantum mechanical resonances and more. Examples show that high-level experiments and theory must work closely together.
Density functional theory in quantum chemistry
Tsuneda, Takao
2014-01-01
This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
Quantum feedback control and classical control theory
Doherty, Andrew C.; Habib, Salman; Jacobs, Kurt; Mabuchi, Hideo; Tan, Sze M.
2000-01-01
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential.
Higgs Effective Field Theories
2016-01-01
The main focus of this meeting is to present new theoretical advancements related to effective field theories, evaluate the impact of initial results from the LHC Run2, and discuss proposals for data interpretation/presentation during Run2. A crucial role of the meeting is to bring together theorists from different backgrounds and with different viewpoints and to extend bridges towards the experimental community. To this end, we would like to achieve a good balance between senior and junior speakers, enhancing the visibility of younger scientists while keeping some overview talks.
Artin, Emil
2009-01-01
This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians. In this revised edition, two mathematical additions complementing the exposition in the original text are made. The new edition also contains several new foot
Devries, P. L.; George, T. F.
1978-01-01
The problem of two atoms colliding in the presence of an intense radiation field, such as that of a laser, is investigated. The radiation field, which couples states of different electronic symmetry, is described by the number state representation while the electronic degrees of freedom (plus spin-orbit interaction) are discussed in terms of a diabatic representation. The total angular momentum of the field-free system and the angular momentum transferred by absorption (or emission) of a photon are explicitly considered in the derivation of the coupled scattering equations. A model calculation is discussed for the Xe + F collision system.
Out-of-equilibrium quantum field dynamics in external fields
Energy Technology Data Exchange (ETDEWEB)
Cao, F.J. [Universidad Complutense de Madrid, Departamento Fisica Atomica, Molecular y Nuclear, Madrid (Spain); LERMA, Observatoire de Paris, Laboratoire Associe au CNRS UMR 8112, Paris (France)
2007-03-15
The quantum dynamics of the symmetry-broken {lambda}({phi} {sup 2}){sup 2} scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J{yields}-J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken {lambda}({phi}{sup 2}){sup 2} scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures. (orig.)
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-01
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Doyen, G.; Drakova, D.
2015-08-01
We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle-wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: (i) There is a chooser mechanism for the selection of the localization site. (ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. (iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. (iv) The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. (v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Tests of alternative quantum theories with neutrons
Energy Technology Data Exchange (ETDEWEB)
Sponar, S.; Durstberger-Rennhofer, K.; Badurek, G.; Hasegawa, Y. [Atominstitut, Vienna University of Technology (Austria); Klepp, J. [Faculty of Physics, University of Vienna (Austria); Schmitzer, C.; Bartosik, H. [CERN, Geneve (Switzerland)
2014-12-04
According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
Toward a physical theory of quantum cognition.
Takahashi, Taiki
2014-01-01
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed. Copyright © 2013 Cognitive Science Society, Inc.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework
Directory of Open Access Journals (Sweden)
Diederik eAerts
2016-03-01
Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Energy Technology Data Exchange (ETDEWEB)
Pastore, S. [University of South Carolina; Wiringa, Robert B. [ANL; Pieper, Steven C. [ANL; Schiavilla, Rocco [Old Dominion U., JLAB
2014-08-01
We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.
Cutkosky rules for superstring field theory
Energy Technology Data Exchange (ETDEWEB)
Pius, Roji [Perimeter Institute for Theoretical Physics,Waterloo, ON N2L 2Y5 (Canada); Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)
2016-10-06
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Quantum theory of laser-stimulated desorption
Slutsky, M. S.; George, T. F.
1978-01-01
A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.
Theory and application of quantum molecular dynamics
Zeng Hui Zhang, John
1999-01-01
This book provides a detailed presentation of modern quantum theories for treating the reaction dynamics of small molecular systems. Its main focus is on the recent development of successful quantum dynamics theories and computational methods for studying the molecular reactive scattering process, with specific applications given in detail for a number of benchmark chemical reaction systems in the gas phase and the gas surface. In contrast to traditional books on collision in physics focusing on abstract theory for nonreactive scattering, this book deals with both the development and the appli
Relativity, symmetry and the structure of quantum theory I Galilean quantum theory
Klink, William H
2015-01-01
Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features: • Meaning and significance of the term of relativity; discussion of the principle of relativity. • Relation of symmetry to relati...
Biava, Pier Mario; Burigana, Fabio; Germano, Roberto; Kurian, Philip; Verzegnassi, Claudio; Vitiello, Giuseppe
2017-09-20
A long history of research has pursued the use of embryonic factors isolated during cell differentiation processes for the express purpose of transforming cancer cells back to healthy phenotypes. Recent results have clarified that the substances present at different stages of cell differentiation-which we call stem cell differentiation stage factors (SCDSFs)-are proteins with low molecular weight and nucleic acids that regulate genomic expression. The present review summarizes how these substances, taken at different stages of cellular maturation, are able to retard proliferation of many human tumor cell lines and thereby reprogram cancer cells to healthy phenotypes. The model presented here is a quantum field theory (QFT) model in which SCDSFs are able to trigger symmetry breaking processes during cancer development. These symmetry breaking processes, which lie at the root of many phenomena in elementary particle physics and condensed matter physics, govern the phase transitions of totipotent cells to higher degrees of diversity and order, resulting in cell differentiation. In cancers, which share many genomic and metabolic similarities with embryonic stem cells, stimulated re-differentiation often signifies the phenotypic reversion back to health and non-proliferation. In addition to acting on key components of the cellular cycle, SCDSFs are able to reprogram cancer cells by delicately influencing the cancer microenvironment, modulating the electrochemistry and thus the collective electrodynamic behaviors between dipole networks in biomacromolecules and the interstitial water field. Coherent effects in biological water, which are derived from a dissipative QFT framework, may offer new diagnostic and therapeutic targets at a systemic level, before tumor instantiation occurs in specific tissues or organs. Thus, by including the environment as an essential component of our model, we may push the prevailing paradigm of mutation-driven oncogenesis toward a closer
Indices for 6 dimensional superconformal field theories
Kim, Seok; Lee, Kimyeong
2017-11-01
We review some recent developments in the 6 dimensional (2, 0) superconformal field theories, focusing on their Bogomol’nyi-Prasad-Sommerfield (BPS) spectra in the Coulomb and symmetric phases computed by various Witten indices. We shall discuss the instanton partition function of 5d maximal super-Yang-Mills theory, and the 6d superconformal index. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed Pestun and Zabzine) which contains 17 chapters available at [1].
BRST quantization of superstring field theory
Energy Technology Data Exchange (ETDEWEB)
Bochicchio, M.
1987-12-03
We write the gauge fixed action which arises in the quantization of Witten's string field theory in a linear gauge, in a form which applies to both the superstring and the bosonic string. The corresponding BRST transformation is nilpotent only on-shell. We construct also an off-shell nilpotent BRST transformation which formally leaves invariant the quantum effective action. This BRST transformation has a geometrical interpretation which could allow to describe the gauge anomalies of the superstring field theory as the nontrivial cohomology of the BRST charge via the Wess-Zumino consistency condition.
Closed superstring field theory and its applications
de Lacroix, Corinne; Erbin, Harold; Kashyap, Sitender Pratap; Sen, Ashoke; Verma, Mritunjay
2017-10-01
We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 noncompact space-time dimensions, but suffers from the usual infrared divergences when the number of noncompact space-time dimensions is 4 or less.
Ghatak, K.P.; Bhattacharya, S.; Bhowmik, S.; Benedictus, R.; Choudhury, S.
2008-01-01
We study thermoelectric power under strong magnetic field (TPM) in carbon nanotubes (CNTs) and quantum wires (QWs) of nonlinear optical, optoelectronic, and related materials. The corresponding results for QWs of III-V, ternary, and quaternary compounds form a special case of our generalized
A simple proof of orientability in colored group field theory.
Caravelli, Francesco
2012-01-01
Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.
Lütkenhaus, N.; Shields, A. J.
2009-04-01
descriptions and are based on observable tests during the run of QKD sessions. It is now 25 years since the first proposal for QKD was published and 20 since the first experimental realization. The intervening years have brought several technological and theoretical advances, which have driven new insights into the application of quantum theory to the wider field of information technology. We are looking forward to the new twists and turns this field will take in the next 25 years! Focus on Quantum Cryptography: Theory and Practice Contents Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space A Leverrier, E Karpov, P Grangier and N J Cerf Optical networking for quantum key distribution and quantum communications T E Chapuran, P Toliver, N A Peters, J Jackel, M S Goodman, R J Runser, S R McNown, N Dallmann, R J Hughes, K P McCabe, J E Nordholt, C G Peterson, K T Tyagi, L Mercer and H Dardy Proof-of-concept of real-world quantum key distribution with quantum frames I Lucio-Martinez, P Chan, X Mo, S Hosier and W Tittel Composability in quantum cryptography Jörn Müller-Quade and Renato Renner Distributed authentication for randomly compromised networks Travis R Beals, Kevin P Hynes and Barry C Sanders Feasibility of 300 km quantum key distribution with entangled states Thomas Scheidl, Rupert Ursin, Alessandro Fedrizzi, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Robert Prevedel, Lothar Ratschbacher, Johannes Kofler, Thomas Jennewein and Anton Zeilinger Decoy-state quantum key distribution with both source errors and statistical fluctuations Xiang-Bin Wang, Lin Yang, Cheng-Zhi Peng and Jian-Wei Pan High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres D Stucki, N Walenta, F Vannel, R T Thew, N Gisin, H Zbinden, S Gray, C R Towery and S Ten Topological optimization of quantum key distribution networks R Alléaume, F Roueff, E Diamanti and N Lütkenhaus The SECOQC quantum key
Quantum Gravity Effects in Scalar, Vector and Tensor Field Propagation
Dutta, Anindita
Quantum theory of gravity deals with the physics of the gravitational field at Planck length scale (10-35 m). Even though it is experimentally hard to reach the Planck length scale, on can look for evidence of quantum gravity that is detectable in astrophysics. In this thesis, we try to find effects of loop quantum gravity corrections on observable phenomena. We show that the quantum fluctuation strain for LIGO data would be 10 -125 on the Earth. Th correction is, however, substantial near the black hole horizon. We discuss the effect of this for scalar field propagation followed by vector and tensor fields. For the scalar field, the correction introduces a new asymmetry; for the vector field, we found a new perturbation solution and for the tensor field, we found the corrected Einstein equations which are yet to solve. These will affect phenomena like Hawking radiation, black hole entropy and gravitational waves.
Quantum reality theory and philosophy
Allday, Jonathan
2009-01-01
PrefaceIntroductionAuthorPart I Our First Quantum Object: Light Some Opening Thoughts A Little Light Reading Lasers and Video Cameras Photons An Interference Experiment with Photons Interference as a Wave Effect Mach-Zehnder with Photons Delayed Choice Summary Endnotes Interlude 1: Another Interference Experiment Particles Electrons The Electron Gun The Stern-Gerlach Experiment Turning Things Round Things Get More Puzzling So, Where Did It Go? What Does It All Mean? Some Indications with Other Particles The Long and the Short of It Summary Endnotes Quantum States Where Are We Now? Describing C
Binary systems from quantum cluster equilibrium theory.
Brüssel, Marc; Perlt, Eva; Lehmann, Sebastian B C; von Domaros, Michael; Kirchner, Barbara
2011-11-21
An extension of the quantum cluster equilibrium theory to treat binary mixtures is introduced in this work. The necessary equations are derived and a possible implementation is presented. In addition an alternative sampling procedure using widely available experimental data for the quantum cluster equilibrium approach is suggested and tested. An illustrative example, namely, the binary mixture of water and dimethyl sulfoxide, is given to demonstrate the new approach. A basic cluster set is introduced containing the relevant cluster motifs. The populations computed by the quantum cluster equilibrium approach are compared to the experimental data. Furthermore, the excess Gibbs free energy is computed and compared to experiments as well.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
[Discussion on quantum entanglement theory and acupuncture].
Wang, Jun; Wu, Bin; Chen, Sheng
2017-11-12
The quantum entanglement is a new discovery of modern physics and has drawn a widely attention in the world. After learning the quantum entanglement, the authors have found that many characteristics of quantum are reflected in TCM, acupuncture theory and clinical practice. For example, the quantum entanglement phenomenon is mutually verified with the holism, yinyang doctrine, the theory of primary, secondary, root and knot in TCM, etc. It can be applied to interpret the clinical situations which is difficult to be explained in clinical practice, such as the instant effect of acupuncture, multi-point stimulation in one disorder and the points with specific effects. On the basis of the discovery above, the quantum entanglement theory achieved the mutual treatment among the relatives in acupuncture clinical practice and the therapeutic effects were significant. The results suggest that the coupling relationship in quantum entanglement presents between the diseases and the acupoints in the direct relative. The authors believe that the discovery in this study contributes to the exploration on the approaches to the acupuncture treatment in clinical practice and enrich the ideas on the disease prevention.
Gauge field theories spin one and spin two : 100 years after general relativity
Scharf, Gunter
2016-01-01
One of the main problems of theoretical physics concerns the unification of gravity with quantum theory. This monograph examines unification by means of the appropriate formulation of quantum gauge invariance. Topics include free fields, causal perturbation theory, spin-1 gauge theories involving both massless and massive gauge fields, spin-2 gauge theories, and non-geometric general relativity.
Field theory, disorder and simulations
Parisi, Giorgio
1992-01-01
This volume is a collection of lectures and selected papers by Giorgio Parisi on the subjects of Field Theory (perturbative expansions, nonperturbative phenomena and phase transitions), Disordered Systems (mainly spin glasses) and Computer Simulations (lattice gauge theories).The basic problems discussed in the Field Theory section concern the interplay between perturbation theory and nonperturbative phenomena which are present when one deals with infrared or ultraviolet divergences or with nonconvergent perturbative expansions. The section on Disordered Systems contains a complete discussion
Quantum mechanics of 4-derivative theories
Salvio, Alberto
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalisable wave functions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
The physical principles of the quantum theory
Heisenberg, Werner Karl
1930-01-01
The contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg. His matrix theory is one of the bases of modern quantum mechanics, while his ""uncertainty principle"" has altered our whole philosophy of science.In this classic, based on lectures delivered at the University of Chicago, Heisenberg presents a complete physical picture of quantum theory. He covers not only his own contributions, but also those of Bohr, Dirac, Bose, de Broglie, Fermi, Einstein, Pauli, Schrodinger, Somerfield, Rupp, ·Wilson, Germer, and others
Quantum mechanics of 4-derivative theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
A categorical framework for quantum theory
Energy Technology Data Exchange (ETDEWEB)
Filk, T. [Institute for Physics, University of Freiburg (Germany); Parmenides Center for the Study of Thinking, Muenchen (Germany); Mueller, A. von [Parmenides Center for the Study of Thinking, Muenchen (Germany); Institute for Philosophy, University of Munich (Germany); SISSA, Trieste (Italy)
2010-11-15
Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear-sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the ''status nascendi'' of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non-sequential time and an extended present which seems to be relevant for a quantum theory of (space)-time. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Inst. de Matematica. Dept. de Matematica Aplicada]. E-mail: botelho.luiz@ig.com.br
2008-07-01
We analyze the triviality-quantum decoherence of Euclidean quantum chromodynamics in the gauge invariant quark current sector in the presence of an external U ({infinity}) flavor constant charged white noise reservoir. (author)
Quantum Theory without Planck's Constant
Ralston, John P.
2012-01-01
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long reference to experiment, review shows that Planck's constant cannot be obtained from the data of Ryberg, Davisson and Germer, Compton, or that used by Planck himself. In the new approach Planck's constant is tied to macroscopic conventions of Newtonian origin, wh...
Quantum Computation and Information From Theory to Experiment
Imai, Hiroshi
2006-01-01
Recently, the field of quantum computation and information has been developing through a fusion of results from various research fields in theoretical and practical areas. This book consists of the reviews of selected topics charterized by great progress and cover the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.
Scattering theory the quantum theory of nonrelativistic collisions
Taylor, John R
2006-01-01
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic p
A geometrical approach to two-dimensional Conformal Field Theory
Dijkgraaf, Robertus Henricus
1989-01-01
This thesis is organized in the following way. In Chapter 2 we will give a brief introduction to conformal field theory along the lines of standard quantum field theory, without any claims to originality. We introduce the important concepts of the stress-energy tensor, the Virasoro algebra, and
Introducing quantum theory a graphic guide
McEvoy, J P
2013-01-01
Quantum theory confronts us with bizarre paradoxes which contradict the logic of classical physics. At the subatomic level, one particle seems to know what the others are doing, and according to Heisenberg's "uncertainty principle", there is a limit on how accurately nature can be observed. And yet the theory is amazingly accurate and widely applied, explaining all of chemistry and most of physics. "Introducing Quantum Theory" takes us on a step-by-step tour with the key figures, including Planck, Einstein, Bohr, Heisenberg and Schrodinger. Each contributed at least one crucial concept to the theory. The puzzle of the wave-particle duality is here, along with descriptions of the two questions raised against Bohr's "Copenhagen Interpretation" - the famous "dead and alive cat" and the EPR paradox. Both remain unresolved.
Field Theory for Multiple Integrals
Zelikin, M.
2009-01-01
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature of bundles induced by a field of extremals are calculated.
Probing noncommutative theories with quantum optical experiments
Directory of Open Access Journals (Sweden)
Sanjib Dey
2017-11-01
Full Text Available One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.
Quantum fields from the Hubble to the Planck scale
Kachelriess, Michael
2017-01-01
This book introduces quantum field theory, together with its most important applications to cosmology and astroparticle physics, in a coherent framework. The path integral approach is employed right from the start, and the use of Green functions and generating functionals is illustrated first in quantum mechanics and then in scalar field theory. Massless spin one and two fields are discussed on an equal footing, and gravity is presented as a gauge theory in close analogy with the Yang-Mills case. Concepts relevant to modern research such as helicity methods, effective theories, decoupling, or the stability of the electroweak vacuum are introduced. Various applications such as topological defects, dark matter, baryogenesis, processes in external gravitational fields, inflation and black holes help students to bridge the gap between undergraduate courses and the research literature.
Boolean Approach to Dichotomic Quantum Measurement Theories
Energy Technology Data Exchange (ETDEWEB)
Nagata, K. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Nakamura, T. [Keio University, Yokohama (Japan); Batle, J. [Universitat de les Illes Balears, Balearic Islands (Spain); Abdalla, S. [King Abdulaziz University Jeddah, Jeddah (Saudi Arabia); Farouk, A. [Al-Zahra College for Women, Muscat (Egypt)
2017-02-15
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or −1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
The g-theorem and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2016-10-25
We study boundary renormalization group flows between boundary conformal field theories in 1+1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Quantum theory, deformation and integrability
Carroll, R
2000-01-01
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between qua
Theory of controlled quantum dynamics
Energy Technology Data Exchange (ETDEWEB)
De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio [Dipartimento di Fisica, Universita di Salerno, and INFN, Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy)
1997-06-07
We introduce a general formalism to obtain localized quantum wavepackets as dynamically controlled systems, in the framework of Nelson stochastic quantization. We show that in general the control is linear, and it amounts to introducing additional time-dependent terms in the potential. In this way one can construct for general systems either coherent packets following classical motion with constant dispersion, or coherent packets following classical motion whose time-dependent dispersion remains bounded for all times. We show that in the operatorial language our scheme amounts to introducing a suitable generalization to arbitrary potentials of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator. (author)
Class field theory from theory to practice
Gras, Georges
2003-01-01
Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant (/cal T) p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory. In the corrected 2nd printing 2005, the author improves s...
Is quantum theory compatible with special relativity?
Indian Academy of Sciences (India)
Condense Matter and Statistical Physics, The Abdul Salam ICTP, Trieste, Italy; Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran; Perimeter Institute for Theoretical Physics, Waterloo, Canada; Department of ...