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Sample records for bohr-sommerfeld quantum theory

  1. On Bohr-Sommerfeld bases

    International Nuclear Information System (INIS)

    This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of Borthwick-Paul-Uribe, in which every vector of a BS basis is determined by some half-weight Legendrian distribution coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to the bases of theta functions) is that we can use the powerful methods of asymptotic analysis of quantum states. This shows that Bohr-Sommerfeld bases are quasiclassically unitary. Thus we can apply these bases to compare the Hitchin connection and the KZ connection defined by the monodromy of the Knizhnik-Zamolodchikov equation in the combinatorial theory

  2. The Bohr-Sommerfeld atom theory. Sommerfeld's extension of Bohr's atomic model 1915/16

    International Nuclear Information System (INIS)

    In December 6th 1915 and January 8th 1916 Arnold Sommerfeld put the Bavarian Academy of Sciences two treatises in the amount of 75 printed pages before, by which he extended Bohr's atomic model from the year 1913 to the Bohr-Sommerfeld atom theory. In Sommerfeld's collected works only the publication submitted 1916 by Sommerfeld in the Annals of Physics about this is found.''My spectral lines are finally printed in the Academy to the impure. In the Annals they will appear in purer form'', so Sommerfeld has announced in this publication in February 10th 1916 to the editor of the Annals of Physics. From the science-historical view however for the extension of Bohr's atom theory just the Academy-treatises published before the purification process are of special interest. To the reproduction of these Academy-treatises an extensive physics-historical essay is prepended.

  3. Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles

    DEFF Research Database (Denmark)

    Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina

    Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n...

  4. Area in phase space as determiner of transition probability: Bohr-Sommerfeld bands, Wigner ripples, and Fresnel zones

    International Nuclear Information System (INIS)

    We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both-to a squeeze in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner function as quantum update of B-S band and near-zone Fresnel diffraction as mockup Wigner function

  5. Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant

    Energy Technology Data Exchange (ETDEWEB)

    Thylwe, Karl-Erik [KTH-Mechanics, Royal Institute of Technology, S-10044 Stockholm (Sweden); McCabe, Patrick [CCDC, 12 Union Road, CB2 1EZ Cambridge (United Kingdom)

    2013-05-15

    It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.

  6. Quantum-Classical Connection for Hydrogen Atom-Like Systems

    Science.gov (United States)

    Syam, Debapriyo; Roy, Arup

    2011-01-01

    The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…

  7. Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

    Science.gov (United States)

    Miller, William H; Cotton, Stephen J

    2016-08-28

    It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements. PMID:27586896

  8. Irreversibility and quantum mechanics

    International Nuclear Information System (INIS)

    Quantum mechanisms has a dual structure: while Schroedinger equation corresponds to a deterministic and time-reversible description, measurement introduces irreversibility and stochasticity. This contrasts with the Bohr-Sommerfeld-Einsten theory, in which transitions between quantum states are associated with spontaneous and induced transitions, defined in terms of a stochastic process. A new form of quantum theory is summarized here, which contains an intrinsic form of irreversibility, independent of observation

  9. Quantum de Sitter Space-Time and the Dark Energy

    CERN Document Server

    Liu, Liao

    2007-01-01

    Three years ago, we introduced a new way to quantize the static Schwarzschild black hole(SSBH), there the SSBH was first treated as a single periodic Euclidean system and then the Bohr-Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole.[1] Now in this short report, we try to extend the above method to quantize the static de Sitter(SDS) space-time and establish a quantum theory of both SDS space and dark energy.

  10. Quantum de Sitter Spacetime and Energy Density Contributed from the Cosmological Constant

    Institute of Scientific and Technical Information of China (English)

    LIU Liao

    2008-01-01

    @@ Previously we introduce a new way to quantize the static Schwarzschild black hole (SSBH), there the SSBH was first treated as a single periodic Euclidean system and then the Bohr-Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole [Chin. Phys. Lett. (2004) 21 1887]. Here we try to extend the above method to quantize the static de Sitter (SDS) spacetime and establish a quantum theory of both SDS space and the energy density contributed from the cosmological constant.

  11. Theory of superfluidity macroscopic quantum waves

    International Nuclear Information System (INIS)

    A new description of superfluidity is proposed, based upon the fact that Bogoliubov's theory of superfluidity exhibits some so far unsuspected macroscopic quantum waves (MQWs), which have a topological nature and travel within the fluid at subsonic velocities. To quantize the bounded quasi-particles the field theoretic version of the Bohr-Sommerfeld quantization rule, is employed and also resort to a variational computation. In an instantaneous configuration the MQWs cut the condensate into blocks of phase, providing, by analogy with ferromagnetism, a nice explanation of what could be the lambda-transition. A crude estimate of the critical temperature gives T sub(c) approximately equal to 2-4K. An attempt is made to understand Tisza's two-fluid model in terms of the MQWs, and we rise the conjecture that they play an important role in the motion of second. We present also a qualitative prediction concerning to the behavior of the 'phononroton' peak below 1.0K, and propose two experiments to look for MQWs

  12. Rise and fall of the old quantum theory

    CERN Document Server

    Bucher, Manfred

    2008-01-01

    The old quantum theory of Bohr and Sommerfeld was abandonned for the wrong reason. Its contradictions were caused not by the orbit concept but by a mental barrier--the inconceivability that an electron might collide with the atomic nucleus. Removing that barrier resolves the theory's main failures--incorrect orbital momenta, He atom, H2+ molecule ion. The inclusion of electron oscillations through the nucleus--a concept called "Coulomb oscillator"--renders the old quantum theory consistent with quantum mechanics (although devoid of wave character). The triple success of the Bohr-Sommerfeld model is its correct description of the H atom (and one-electron ions) concerning (1) the energy levels Enl, (2) the orbital angular momenta Lnl--if corrected as Lnl^2 = l(l+1) hbar^2 and with the Coulomb oscillator included--and (3) the orbits' space quantization--with (Lnl)z = ml hbar. These achievements are succinctly represented by the principal, angular and magnetic quantum numbers (n, l, ml) and visualized by orbital ...

  13. On the quantum levels of isolated spherically symmetric gravitational systems

    CERN Document Server

    Kastrup, H A

    1996-01-01

    The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\\tau/\\hbar) with respect to their continuous masses M and the proper time \\tau of observers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr- Sommerfeld quantisation in atomic physics. The two approaches can be related by postulating periodic boundary conditions in time for the plane waves and by iden- tifying the period \\Delta in real time with the period \\Delta_H = 8\\pi GM/c^3 in Euclidean time. This yields the mass spectrum M_n = (1/2)\\sqrt{n}m_P, n=1,2,...

  14. Quantum Theory

    CERN Document Server

    Manning, Phillip

    2011-01-01

    The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.

  15. Discrete-charge quantum circuits in semiclassical approach

    OpenAIRE

    Utreras-Díaz, C.A.; J. C. Flores

    2006-01-01

    We discuss a new approach to describe mesoscopic systems, based on the ideas of quantum electrical circuits with charge discreteness. This approach has allowed us to propose a simple alternative descriptions of some mesoscopic systems, with interesting results for some mesoscopic systems. In his work, we show that the application of the Bohr-Sommerfeld quantization rules to the Quantum $LC$ circuit with discrete charge allows us to easily reproduce previous results.

  16. Quantum theory

    International Nuclear Information System (INIS)

    This textbook for students of physics is oriented in the selection of matter by the contents of a two-semester course about quantum theory. Thereby the foundations of quantum theory, among them the quantum-mechanical measurement process, the mathematical formalism, and Bell's inequalities, are extensively treated. Also modern concepts like feynman's path integral are regarded. This work is equally suited for a self-study, as course-accompanying lecture, and for preparations of examina. Application examples, supplementary explanations, and numerous illustration take car for a good understanding of the theoretical contents

  17. Quantum theory

    CERN Document Server

    Bohm, David

    1951-01-01

    This superb text by David Bohm, formerly Princeton University and Emeritus Professor of Theoretical Physics at Birkbeck College, University of London, provides a formulation of the quantum theory in terms of qualitative and imaginative concepts that have evolved outside and beyond classical theory. Although it presents the main ideas of quantum theory essentially in nonmathematical terms, it follows these with a broad range of specific applications that are worked out in considerable mathematical detail. Addressed primarily to advanced undergraduate students, the text begins with a study of t

  18. Discretization on the cosmic scale inspired from the Old Quantum Mechanics

    OpenAIRE

    Agnese, A. G.; Festa, R

    1998-01-01

    The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are used to calculate a few mechanical quantities pertinent to the periodic motions of celestial bodies. Several values have been obtained which result in reasonable agreement with the corresponding experimental data. A gravitational dimensionless structure const...

  19. Quantum algorithmic information theory

    OpenAIRE

    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...

  20. Quantum biological information theory

    CERN Document Server

    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...

  1. Quantum Theory

    Science.gov (United States)

    Murdin, P.

    2000-11-01

    A theory based on the premise that, on the microscopic scale, physical quantities have discrete, rather than a continuous range of, values. The theory was devised in the early part of the twentieth century to account for certain phenomena that could not be explained by classical physics. In 1900, the German physicist, Max Planck (1858-1947), was able precisely to describe the previously unexplaine...

  2. Theory of Quantum Friction

    OpenAIRE

    Silveirinha, Mario G.

    2013-01-01

    Here, we develop a comprehensive quantum theory for the phenomenon of quantum friction. Based on a theory of macroscopic quantum electrodynamics for unstable systems, we calculate the quantum expectation of the friction force, and link the friction effect to the emergence of system instabilities related to the Cherenkov effect. These instabilities may occur due to the hybridization of particular guided modes supported by the individual moving bodies, and selection rules for the interacting mo...

  3. Algebraic quantum field theory

    International Nuclear Information System (INIS)

    The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)

  4. Quantum electronics basic theory

    CERN Document Server

    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

  5. Quantum relativity theory

    International Nuclear Information System (INIS)

    A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is argued that the quantum space-time models of Banai introduced in an earlier paper is formulated in terms of Davis' quantum relativity. Then it is shown that the recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce in a consistent way the quantum space-time model (the 'canonically quantized Minkowski space') proposed by Banai earlier. The main new aspect of the quantum mechanics of the quantum relativistic particles is, in this model of space-time, that it provides a true mass eigenvalue problem and, that the excited mass states of such particles can be interpreted as classifically relativistic (massive) quantum particles ('elementary particles'). The question of field theory over quantum relativistic models of space-time is also discussed. Finally, it is suggested that 'quarks' should be considered as quantum relativistic particles. (author)

  6. Quantum microeconomics theory

    OpenAIRE

    Ledenyov, Dimitri O.; Ledenyov, Viktor O.

    2015-01-01

    The research article presents the highly innovative theoretical research results: 1) the new quantum microeconomics theory in the quantum econophysics science is formulated; the idea on the existence of the discrete-time induced quantum transitions of firm’s earnings (the firm’s value) in the quantum microeconomics theory in the quantum econophysics science is proposed; 2) the formulas (1, 2) to compute the firm’s discrete-time EBITDA (the firm’s value) changes at the different time moments i...

  7. Theory of quantum friction

    International Nuclear Information System (INIS)

    Here, we develop a comprehensive quantum theory for the phenomenon of quantum friction. Based on a theory of macroscopic quantum electrodynamics for unstable systems, we calculate the quantum expectation of the friction force at zero temperature, and link the friction effect to the emergence of system instabilities related to the Cherenkov effect. These instabilities may occur due to the hybridization of particular guided modes supported by the individual moving bodies, and selection rules for the interacting modes are derived. It is proven that the quantum friction effect can take place even when the interacting bodies are lossless and made of nondispersive dielectrics. (paper)

  8. Quantum Game Theory

    OpenAIRE

    Lassig, Michael

    2011-01-01

    A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by quantum Nash equilibria, a generalization of the well-known Nash equilibrium points in classical game theory. The implications of this theory for biological systems are discussed in detail.

  9. Quantum Theory and Beyond

    Science.gov (United States)

    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

  10. Reverse Engineering Quantum Field Theory

    OpenAIRE

    Oeckl, Robert

    2012-01-01

    An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.

  11. Almost quantum theory

    OpenAIRE

    Schumacher, Benjamin; Westmoreland, Michael D.

    2012-01-01

    Modal quantum theory (MQT) is a "toy model" of quantum theory in which amplitudes are elements of a general field. The theory predicts, not the probabilities of a measurement result, but only whether or not a result is possible. In this paper we review MQT and extend it to include mixed states, generalized measurements and open system dynamics. Even though MQT does not have density operators, superoperators or any concept of "positivity", we can nevertheless establish a precise analogue to th...

  12. Effective quantum field theories

    International Nuclear Information System (INIS)

    Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)

  13. Quantum field theory

    International Nuclear Information System (INIS)

    This book is composed of 10 chapters. It starts by introducing classical principle of action. It adds quantal principle of action, which is divided into two cases that the degree of freedom is limited and limitless. It continues to basic quantum field theories, Green's function and functional differential equation toward green sources, solvable models, formal value of functional differential equation: quantization method of path integral formulation, approximate calculation of greens function, Representation Method of Schrodinger of quantum field theory and expansion of quantum field theory.

  14. Quantum Gravity as Topological Quantum Field Theory

    OpenAIRE

    Barrett, John W.

    1995-01-01

    The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.

  15. Quantum theory of fields

    CERN Document Server

    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

  16. Quantum kinetic theory

    CERN Document Server

    Bonitz, Michael

    2016-01-01

    This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

  17. Quantum field theory

    CERN Document Server

    Alvarez-Gaumé, Luís

    1996-01-01

    Quantum Field Theory provides the most fundamental language known to express the fundamental laws of Nature. It is the consequence of trying to describe physical phenomena within the conceptual framework of Quantum Mechanics and Special Relativity. The aim of these lectures will be to present a number of concepts and methods in the subject which many of us find difficult to understand. They may include (depending on time) : the need to introduce quantum fields, the realization of symmetries, the renormalization group, non-perturbative phenomena, infrared divergences and jets, etc. Some familiarity with the rudiments of Feynman diagrams and relativistic quantum mechanics will be appreciated.

  18. Discrete quantum theories

    International Nuclear Information System (INIS)

    We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x2 + 1 = 0, and thus permits an elegant complex representation of the extended field by adjoining i=√(−1). Quantum theories over these fields recover much of the structure of conventional quantum theory except for the condition that vanishing inner products arise only from null states; unnaturally strong computational power may still occur. Finally, we are led to consider one more framework, with further restrictions on the finite fields, that recovers a local transitive order and a locally-consistent notion of inner product with a new notion of cardinal probability. In this framework, conventional quantum mechanics and quantum computation emerge locally (though not globally) as the size of the underlying field increases. Interestingly, the framework allows one to choose separate finite fields for system description and for measurement: the size of the first field quantifies the resources needed to describe the system and the size of the second quantifies the resources used by the observer. This resource-based perspective potentially provides insights into quantitative measures for actual computational power, the complexity of quantum system definition and evolution, and the independent question of the cost of the measurement process. (paper)

  19. Quantum group gauge theory on quantum spaces

    OpenAIRE

    Brzezinski, Tomasz; Majid, Shahn

    1992-01-01

    We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-co...

  20. Quantum Field Theory without Divergences: Quantum Spacetime

    OpenAIRE

    Gadiyar, G. H.

    1994-01-01

    A fundamental length is introduced into physics in a way which respects the principles of relativity and quantum field theory. This improves the properties of quantum field theory: divergences are removed. How to quantize gravity is also indicated. When the fundamental length tends to zero the present version of quantum field theory is recovered.

  1. Superluminality in Quantum Theory

    OpenAIRE

    Fantasia, Giovanni Andrea

    2003-01-01

    In the present work we investigate the possibility of superluminal information transmission in quantum theory. We give simple and general arguments to prove that the general structure (Hilbert's space plus instantaneous state reduction) of the theory allows the existence of superluminal communication. We discuss how this relates with existing no-signalling theorems.

  2. Entropy Spectrum of Black Holes of Heterotic String Theory via Adiabatic Invariance

    Institute of Scientific and Technical Information of China (English)

    Alexis Larra? aga; Luis Cabarique; Manuel Londo? o

    2012-01-01

    Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we investigate the entropy spectroscopy of two black holes of heterotic string theory,the charged GMGHS and the rotating Sen solutions.It is shown that the entropy spectrum is equally spaced in both cases,identically to the spectrum obtained before for Schwarzschild,Reissner-Nordstr?m and Kerr black holes.Since the adiabatic invariance method does not use quasinormal mode analysis,there is no need to impose the small charge or small angular momentum limits and there is no confusion on whether the real part or the imaginary part of the modes is responsible for the entropy spectrum.

  3. Quantum Algorithms for Quantum Field Theories

    OpenAIRE

    Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John

    2012-01-01

    Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling...

  4. Compatible quantum theory

    International Nuclear Information System (INIS)

    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

  5. Quantum group gauge theory on quantum spaces

    International Nuclear Information System (INIS)

    We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces). (orig.)

  6. Dissipative quantum theory: Implications for quantum entanglement

    OpenAIRE

    Rajagopal, A. K.; Rendell, R. W.

    2001-01-01

    Three inter-related topics are discussed here. One, the Lindblad dynamics of quantum dissipative systems; two, quantum entanglement in composite systems and its quantification based on the Tsallis entropy; and three, robustness of entanglement under dissipation. After a brief review of the Lindblad theory of quantum dissipative systems and the idea of quantum entanglement in composite quantum systems illustrated by describing the three particle systems, the behavior of entanglement under the ...

  7. Quantum algorithms for quantum field theories.

    Science.gov (United States)

    Jordan, Stephen P; Lee, Keith S M; Preskill, John

    2012-06-01

    Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052

  8. Quantum Field Theory

    CERN Document Server

    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...

  9. Quantum Field Theory of Fluids

    OpenAIRE

    Gripaios, Ben; Sutherland, Dave

    2015-01-01

    The quantum theory of fields is largely based on studying perturbations around non-interacting, 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 non-interacting 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...

  10. Quantum theory from questions

    CERN Document Server

    Hoehn, Philipp A

    2016-01-01

    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 `catalogue of knowledge' about S; no ontic assumptions are necessary. From the rules we derive the state spaces for N qubits and show that (a) they coincide with the set of density matrices over N qubit Hilbert spaces; (b) states evolve unitarily under the group $\\rm{PSU}(2^N)$ according to the von Neumann evolution equation; and (c) the binary questions by means of which O interrogates the systems corresponds to projective measurements on Pauli operators with outcome probabilities given by the Born rule. Besides offering a novel conceptual perspective on qubit quantum theory, the reconstruction also unravels new structural insights. Namely, we show that, in a quadratic information measure, (d) qubits satisfy informational complementarity inequalities...

  11. Quantum theory from questions

    OpenAIRE

    Hoehn, Philipp A; Wever, Christopher(Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’,, Agia Paraskevi, 15310, Greece)

    2015-01-01

    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 `catalogue 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; (b) states evolve unitarily under the...

  12. Quantum scattering theory

    CERN Document Server

    Kouri, Donald J

    2017-01-01

    This book provides a detailed exposition of quantum scattering theory as applied to chemical physics. It includes the fundamental mathematics of scattering, details of how it applies to atom-molecule, molecule-molecule collisions, as well as collisions with surfaces. A variety of computational methods for solving scattering problems are presented. In addition, some discussion of fully quantal approximations is included. Both inelastic and reactive scattering are treated in detail. Both time-dependent and time-independent approaches to scattering theory and scattering computation are included. The book will reflect the research done over approximately 50 years by the author.

  13. The Quantum Underground: Early quantum theory textbooks

    Science.gov (United States)

    Gearhart, Clayton

    2011-04-01

    Quantum theory had its beginnings in 1900, when Max Planck derived his famous formula for the energy density of black-body radiation. But the early quantum theory textbooks we remember today--for example, those of Arnold Summerfeld (1919), Fritz Reiche (1921), and a shorter Report by James Jeans (1914), did not appear until some years later, and all were written by physicists who were themselves active participants in early quantum theory. Surprisingly, not all early texts fit this pattern. Reiche himself had written a review article on quantum theory for general readers in Die Naturwissenschaften in 1913, long before his research had shifted to quantum topics. And a year later, textbooks by Hermann Sieveking and Sigfried Valentiner treated quantum theory for students and non-specialists, although neither was active in quantum theoretical research. A third and better known author, Owen Richardson, also treated quantum theory in a 1914 book on electromagnetism. I will describe these early and little-known treatments of quantum theory, all of which were written by physicists whose primary research and professional interests lay elsewhere.

  14. Studies in quantum field theory

    International Nuclear Information System (INIS)

    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

  15. Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

    Directory of Open Access Journals (Sweden)

    Jun Tao

    2015-01-01

    Full Text Available In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to Oβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

  16. Quantum computation and complexity theory

    OpenAIRE

    Svozil, K.

    1994-01-01

    The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed.

  17. The Quantum Theory of Fluids

    CERN Document Server

    Gripaios, Ben

    2014-01-01

    The quantum theory of fields is largely based on studying perturbations around non-interacting, 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 non-interacting 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 behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.

  18. Quantum Information Theory - an Invitation

    OpenAIRE

    Werner, R. F.

    2001-01-01

    We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory. The capacities of a quantum channel for classical and for quantum information are defined in a unified scheme, and a mathematical characterization of all teleportation and dense coding schemes is given.

  19. Quantum Information and Relativity Theory

    OpenAIRE

    Peres, Asher; Terno, Daniel R.

    2002-01-01

    Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its description are Kraus matrices and positive operator valued measures (POVMs). Special relativity imposes severe restrictions on the transfer of information between distant systems. Quantum entropy is not a Lorentz covariant concept. Lorentz transformations o...

  20. Theory of interacting quantum fields

    International Nuclear Information System (INIS)

    This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

  1. Quantum Universe Theory

    Science.gov (United States)

    Cunningham, Bruce

    2009-11-01

    The Initial Condition (that which existed prior to the universe) is compared as an infinite thermodynamic system (reservoir and system) to a two-component blackbody system, where one component, composed of unbound bosons, contained a symmetry breaking potential. Symmetry breaking resulted in the moment of inflation in a subsystem (small part) of one component, which in turn ignited an unloading wave. The ensuing Big Bang Unloading Wave created a continuously expanding cavity in that component. The cavity is the universe. Within the expanding unloading wave, the first energy cascade has continuously produced intense plasma effects, superelectric fields, and supermagnetic effects. The intense plasma produces violent pinch effects propelling superelectric-magnetic particles to the speed of light c impacting them within the other component (bound boson Fermi-Dirac particles) as original energy particles representing the apex of the spectral ladder and the beginning of the second energy cascade. Here quench factors freeze persistent superconducting current vibrations into place prior to application of the algorithmic ladder of the quantum field theory time line. Energies evolve to include the formation of std model physics (QM,QED,QCD) general theory of relativity (GRT), special theory (SRT), linear momentum, and angular momentum, etc.

  2. Is Quantum Gravity a Super-Quantum Theory?

    OpenAIRE

    Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu

    2013-01-01

    We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.

  3. The next stage: quantum game theory

    OpenAIRE

    Piotrowski, Edward W.; Jan Sladkowski

    2003-01-01

    Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society.

  4. Quantum Transition-State Theory

    CERN Document Server

    Hele, Timothy J H

    2014-01-01

    This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transition-state theory (RPMD-TST), which was previously considered a heuristic method, and whose results we thereby validate. The key step in deriving a QTST is alignment of the flux and side dividing surfaces in path-integral space to obtain a quantum flux-side time-correlation function with a non-zero $t\\to 0_+$ limit. We then prove that this produces the exact quantum rate in the absence of recrossing by the exact quantum dynamics, fulfilling the requirements of a QTST. Furthermore, strong evidence is presented that this is the only QTST with positive-definite Boltzmann statistics and therefore the pre-eminent method for computation of thermal quantum rates in direct reactions.

  5. The quantum theory of measurement

    CERN Document Server

    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.

  6. Quantum Cosmology: Effective Theory

    OpenAIRE

    Bojowald, Martin

    2012-01-01

    Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge of specific properties of quantum states, it remained difficult to make testable predictions. For quantum cosmology to be part of empirical science, it must allow for a systematic framework in which corrections to well-tested classical equations can be deri...

  7. Recoverability in quantum information theory

    CERN Document Server

    Wilde, Mark M

    2015-01-01

    The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information...

  8. Topics in quantum field theory

    International Nuclear Information System (INIS)

    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

  9. Time, chance and quantum theory

    CERN Document Server

    Sudbery, Anthony

    2016-01-01

    I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.

  10. A Note on Instanton Effects in ABJM Theory

    CERN Document Server

    Wang, Xian-fu; Huang, Min-xin

    2014-01-01

    We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P^1*P^1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.

  11. A note on instanton effects in ABJM theory

    Science.gov (United States)

    Wang, Xian-fu; Wang, Xin; Huang, Min-xin

    2014-11-01

    We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local ℙ1 × ℙ1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.

  12. Quantum Theory is an Information Theory

    Science.gov (United States)

    D'Ariano, Giacomo M.; Perinotti, Paolo

    2016-03-01

    In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

  13. Quantum Theory: Exact or Approximate?

    OpenAIRE

    Adler, Stephen L.; Bassi, Angelo

    2009-01-01

    Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and philosophy. There are two distinct approaches. One is to assume that quantum theory is exact, but that the interpretive postulates need modification, to eliminate apparent contradictions. The second approach is to assume that quantum mechanics is not exact,...

  14. Quantum theory of excess noise

    OpenAIRE

    Bardroff, P. J.; Stenholm, S

    1999-01-01

    We analyze the excess noise in the framework of the conventional quantum theory of laser-like systems. Our calculation is conceptually simple and our result also shows a correction to the semi-classical result derived earlier.

  15. Quantum Game Theory in Finance

    OpenAIRE

    Piotrowski, Edward W.; Jan Sladkowski

    2004-01-01

    This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is also discussed. The review is addressed to non--specialists.

  16. Quantum theory a wide spectrum

    CERN Document Server

    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

  17. Quantum Field Theory in Graphene

    OpenAIRE

    Fialkovsky, I. V.; Vassilevich, D. V.

    2011-01-01

    This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

  18. Quantum Field Theory in (0 + 1) Dimensions

    Science.gov (United States)

    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…

  19. Spinors in Quantum Geometrical Theory

    OpenAIRE

    Galehouse, Daniel C.

    2002-01-01

    Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and may bring about a profound understanding of the mathematical structure of fundamental physics. A program to attempt this is laid out here. Concepts from a known quantum-geometrical theory are reviewed: (1) Classical physics is replaced by a suitable geometr...

  20. Classical and quantum effective theories

    CERN Document Server

    Polonyi, Janos

    2014-01-01

    A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.

  1. Introduction to quantum field theory

    International Nuclear Information System (INIS)

    The lectures appear to be a continuation to the introduction to elementary principles of the quantum field theory. The work is aimed at constructing the formalism of standard particle interaction model. Efforts are made to exceed the limits of the standard model in the quantum field theory context. Grand unification models including strong and electrical weak interactions, supersymmetric generalizations of the standard model and grand unification theories and, finally, supergravitation theories including gravitation interaction to the universal scheme, are considered. 3 refs.; 19 figs.; 2 tabs

  2. Quantum decision theory as quantum theory of measurement

    International Nuclear Information System (INIS)

    We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems

  3. Quantum Dots: Theory

    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.

  4. Quantum Dots: Theory

    OpenAIRE

    Vukmirovic, Nenad

    2010-01-01

    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.

  5. Quantum field theory competitive models

    CERN Document Server

    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...

  6. Fractional statistics and quantum theory

    CERN Document Server

    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

  7. Quantum Hamilton-Jacobi theory.

    Science.gov (United States)

    Roncadelli, Marco; Schulman, L S

    2007-10-26

    Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schrödinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application, we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory. PMID:17995307

  8. Measurement theory in quantum mechanics

    International Nuclear Information System (INIS)

    It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in a natural way in the quantum mechanics theory. There are no longer fundamental differences between macroscopic and microscopic objects, between classical and quantum objects, between observer and object. Thus, discrepancies and paradoxes have disappeared from the conventional quantum mechanics theory. One consequence of the cumulative memory of the particles is that the sum of negentropy plus information is a constant. Using this theory it is also possible to explain the 'paranormal' phenomena and what is their difference from the 'normal' ones

  9. Quantum information and relativity theory

    International Nuclear Information System (INIS)

    This article discusses the intimate relationship between quantum mechanics, information theory, and relativity theory. Taken together these are the foundations of present-day theoretical physics, and their interrelationship is an essential part of the theory. The acquisition of information from a quantum system by an observer occurs at the interface of classical and quantum physics. The authors review the essential tools needed to describe this interface, i.e., Kraus matrices and positive-operator-valued measures. They then discuss how special relativity imposes severe restrictions on the transfer of information between distant systems and the implications of the fact that quantum entropy is not a Lorentz-covariant concept. This leads to a discussion of how it comes about that Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory is, of course, necessary for a consistent description of interactions. Its structure implies a fundamental tradeoff between detector reliability and localizability. Moreover, general relativity produces new and counterintuitive effects, particularly when black holes (or, more generally, event horizons) are involved. In this more general context the authors discuss how most of the current concepts in quantum information theory may require a reassessment

  10. GRAVITATIONAL WAVES AND QUANTUM THEORY

    OpenAIRE

    Trunev A. P.

    2014-01-01

    In this article we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation. Schrödinger conjecture about the Schrödinger wave function and gravitational waves has been proved

  11. [Studies in quantum field theory

    International Nuclear Information System (INIS)

    During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are 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 order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

  12. The Ontology of Quantum Theory

    International Nuclear Information System (INIS)

    An interpretation of the quantum theory is proposed, allowing an explanation of the origins of the theory principles and its mathematical formalism. In contrast to the hitherto interpretations it is based on the ontology assuming existence of omniscience. The interpretation proposed explains - in consistence with the relativity theory - the results of the correlation experiments implying that an unobserved elementary particle does not exist objectively (beyond our consciousness) or that a quantum system makes o non - divisive unity bound through non-spacetime interactions. According to this interpretation, both these possibilities occur simultaneously. (author)

  13. Quantum Link Models and Quantum Simulation of Gauge Theories

    International Nuclear Information System (INIS)

    This lecture is about Quantum Link Models and Quantum Simulation of Gauge Theories. The lecture consists out of 4 parts. The first part gives a brief history of Computing and Pioneers of Quantum Computing and Quantum Simulations of Quantum Spin Systems are introduced. The 2nd lecture is about High-Temperature Superconductors versus QCD, Wilson’s Lattice QCD and Abelian Quantum Link Models. The 3rd lecture deals with Quantum Simulators for Abelian Lattice Gauge Theories and Non-Abelian Quantum Link Models. The last part of the lecture discusses Quantum Simulators mimicking ‘Nuclear’ physics and the continuum limit of D-Theorie models. (nowak)

  14. Propensity, Probability, and Quantum Theory

    Science.gov (United States)

    Ballentine, Leslie E.

    2016-08-01

    Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.

  15. Bohmian Mechanics and Quantum Field Theory

    OpenAIRE

    Duerr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghi, Nino

    2003-01-01

    We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which in particular ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines fo...

  16. Foundations of quantum theory and quantum information applications

    OpenAIRE

    Galvao, Ernesto F.

    2002-01-01

    This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity pr...

  17. Studying quantum field theory

    International Nuclear Information System (INIS)

    The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations of the quantum mechanical conformal group SU(2,2) in the study of gauge fields and their higher spin generalization. A recent revival of the (Bogolubov-)Epstein-Glaser approach to position space renormalization is reviewed including an application to the calculation of residues of primitively divergent graphs. We end up with an optimistic outlook of current developments of analytic methods in perturbative QFT which combine the efforts of theoretical physicists, algebraic geometers and number theorists

  18. An invitation to Quantum Game Theory

    OpenAIRE

    Piotrowski, Edward W.; Jan Sladkowski

    2002-01-01

    Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this context, a new application of the Ising chain model is proposed.

  19. Experimental quantum field theory

    International Nuclear Information System (INIS)

    The CERN-JINR School of Physics is meant to give young experimental physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. This paper presents what the author regards to be the essential minmum of quantum field thoery that should be known to experimental particle physicists. (B.D.)

  20. General covariance and quantum theory

    International Nuclear Information System (INIS)

    The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory

  1. Field theories of quantum gravity

    International Nuclear Information System (INIS)

    Attempts at constructing a satisfactory quantum field theory of gravity have been an active area of research for many years. We shall review various aspects of this problem restricting ourselves to the ''covariant'', rather than the ''canonical'', approach. This still leaves a vast area, and many interesting topics will have to be omitted. We discuss the violation of classical symmetries in quantum theory, i.e. the question of anomalies, and, in particular, gravitational anomalies; the ultraviolet problem in Einstein gravity and its supersymmetric extensions; the renormalizable ''higher derivative'' theory, and the status of the unitarity problem; and the further extension to strings, i.e. extended objects and infinite component field theories, and their ''low energy'' local field theory limit. (author)

  2. A Naturally Renormalized Quantum Field Theory

    OpenAIRE

    Rouhani, S.; Takook, M. V.

    2006-01-01

    It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space togeth...

  3. Quantum network theory

    International Nuclear Information System (INIS)

    A general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits. This approach is capable of dealing with electrical networks having nonlinear or dissipative elements. The techniques are used to analyze a degenerate parametric amplifier, a device capable of generating squeezed coherent state signals. A circuit capable of performing back-action-evading electrical measurements is also discussed. (author)

  4. The quantum field theory interpretation of quantum mechanics

    OpenAIRE

    de la Torre, Alberto C.

    2015-01-01

    It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.

  5. Matrix String Theory As A Generalized Quantum Theory

    OpenAIRE

    Minic, Djordje

    1997-01-01

    Matrix String Theory of Banks, Fischler, Shenker and Susskind can be understood as a generalized quantum theory (provisionally named "quansical" theory) which differs from Adler's generalized trace quantum dynamics. The effective Matrix String Theory Hamiltonian is constructed in a particular fermionic realization of Matrix String Theory treated as an example of "quansical" theory.

  6. 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-½ 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.

  7. Fundamentals of Quantum Information Theory

    OpenAIRE

    Keyl, M.

    2002-01-01

    In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their mathematical description. The second part is focused on a presentation of the quantitative aspects of the theory. Topics discussed in this context include: entanglement measures, channel capacities, relations between both, additivity and continuity propertie...

  8. Finite quantum gauge theories

    Science.gov (United States)

    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).

  9. Discretization on the cosmic scale inspired from the Old Quantum Mechanics

    CERN Document Server

    Agnese, A G

    1998-01-01

    The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are used to calculate a few mechanical quantities pertinent to the periodic motions of celestial bodies. Several values have been obtained which result in reasonable agreement with the corresponding experimental data. A gravitational dimensionless structure constant has been determined, using the data relative to the solar sistem, which allows to quantitatively account for phenomena on a much wider scale. In particular, some information is acquired about the recently discovered extrasolar planetary systems and about the general empirical law which connects the spin of a celestial body with the square of its mass.

  10. Jump processes in quantum theories

    International Nuclear Information System (INIS)

    In this lecture we show that actually the use of jump processes naturally arises in large class of problems and that they are not necessarily associated with a specified representation of the quantum mechanics. In Section 2, we recall the basic structure and properties of this object. In Section 3, we derive an integral representation 'a la Feynman' for the time evolution of the Wigner function by a stochastic flow on the phase space. In Section 4, we use previous representations to discuss the existence of relativistic quantum flow associated with trigonometric models of relativistic quantum field theory. In the last section, we are interested in the classical limit of quantum mechanics time evolution. (orig./HSI)

  11. Quantum Field Theory: Where We Are

    OpenAIRE

    Fredenhagen, Klaus; Rehren, Karl-Henning; Seiler, Erhard

    2007-01-01

    We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.

  12. Interference and inequality in quantum decision theory

    International Nuclear Information System (INIS)

    The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases.

  13. Interference and inequality in quantum decision theory

    Energy Technology Data Exchange (ETDEWEB)

    Cheon, Taksu, E-mail: taksu.cheon@kochi-tech.ac.j [Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan); Takahashi, Taiki, E-mail: ttakahashi@lynx.let.hokudai.ac.j [Laboratory of Social Psychology, Department of Behavioral Science, Faculty of Letters, Hokkaido University, N.10, W.7, Kita-ku, Sapporo 060-0810 (Japan)

    2010-12-01

    The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases.

  14. Interpreting quantum theory a therapeutic approach

    CERN Document Server

    Friederich, Simon

    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'.

  15. Quantum corrections in classicalon theories

    Directory of Open Access Journals (Sweden)

    P. Asimakis

    2015-04-01

    Full Text Available We use the heat kernel in order to compute the one-loop effective action on a classicalon background. We find that the UV divergences are suppressed relative to the predictions of standard perturbation theory in the interior of the classicalon. There is a strong analogy with the suppression of quantum fluctuations in Galileon theories, within the regions where the Vainshtein mechanism operates (discussed in arXiv:1401.2775. Both classicalon and Galileon theories display reduced UV sensitivity on certain backgrounds.

  16. Quantum theory of collective motion

    International Nuclear Information System (INIS)

    This is the third in a series of papers which intends to develop a new microscopic theory capable by itself to determine the ''maximal-decoupled'' collective subspace in the many-particle Hilbert space as well as the collective Hamiltonian specifying the subspace. The fundamental principle to formulate the theory is called the Invariance principle of the Schroedinger equation. The main purpose of this paper is to show that, when we positively utilize the invariance principle, we can directly obtain a quantum theory of collective motion going beyond the random phase approximation. (author)

  17. Time-Symmetrized Counterfactuals in Quantum Theory

    OpenAIRE

    Vaidman, L.

    1998-01-01

    Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I argue here that the apparent contradiction is due to a logical error. I analyze the concept of counterfactuals in quantum theory and introduce time-symmetrized c...

  18. Transfer principle in quantum set theory

    OpenAIRE

    Ozawa, Masanao

    2006-01-01

    In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary vo...

  19. Quasi Hopf quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    In quantum theory, internal symmetries more general than groups are possible. We show that quasi-triangular quasi Hopf algebras G* ('quasi quantum groups') permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators. All this remains true when Drinfeld's axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasi-triangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G* admits a *-operation with certain properties. Invariance properties of Green functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like Uq(sl2) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasi-triangular quasi Hopf algebra G* is canonically associated with Uq(sl2) if qp=1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)

  20. Quantum Shannon Theory

    CERN Document Server

    Preskill, John

    2016-01-01

    This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An early version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this version is substantially revised and expanded. The level of detail is uneven, as I've aimed to provide a gentle introduction, but I've also tried to avoid statements that are incorrect or obscure. Generally speaking, I chose to include topics that are both useful to know and relatively easy to explain; I had to leave out a lot of good stuff, but on the other hand the chapter is already quite long. This is a working draft of Chapter 10, which I will continue to update. See the URL on the title page for further updates and drafts of other chapters, and please send me an email if you notice errors. Eventually, the complete book will be published by Cambridge University Press.

  1. Quantum theory of acoustoelectric interaction

    DEFF Research Database (Denmark)

    Mosekilde, Erik

    1974-01-01

    Within the self-consistent-field approximation, a quantum-mechanical derivation is given for the dielectric response function of an arbitrarily degenerate free-electron gas which is subjected to a drift field. Neglecting in the equation of motion for the one-electron density operator a convection...... 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...

  2. Quantum Field Theory A Modern Perspective

    CERN Document Server

    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...

  3. Beable-Guided Quantum Theories: Generalising Quantum Probability Laws

    CERN Document Server

    Kent, Adrian

    2013-01-01

    We introduce the idea of a {\\it beable-guided quantum theory}. Beable-guided quantum theories (BGQT) are generalisations of quantum theory, inspired by Bell's concept of beables. They modify the quantum probabilities for some specified set of fundamental events, histories, or other elements of quasiclassical reality by probability laws that depend on the realised configuration of beables. For example, they may define an additional probability weight factor for a beable configuration, independent of the quantum dynamics. BGQT can be fitted to observational data to provide foils against which to compare explanations based on standard quantum theory. For example, a BGQT could, in principle, characterise the effects attributed to dark energy or dark matter, or any other deviation from the predictions of standard quantum dynamics, without introducing extra fields or a cosmological constant. The complexity of the beable-guided theory would then parametrise how far we are from a standard quantum explanation. Less co...

  4. Quantum theory of human communication

    OpenAIRE

    Slowikowski, Wojtek; Nielsen, Erik B.

    2004-01-01

    We use notions and techniques of Quantum Field Theory to formulate and investigate basic concepts and mechanisms of human communication. We start with attitudes which correspond to photons frequencies, then we introduce states-of-mind which correspond to wave functions. Finally, by way of the second quantization, we come to states-of-opinions which correspond to states of quantized radiation fields. In the present paper we shall only investigate superpositions of pairs of coherent states (e.g...

  5. Quantum Theory and Time Asymmetry

    OpenAIRE

    Zeh, H. D.

    2003-01-01

    The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as of information about them. The concept of relevance being used in all statistical theories of irreversible thermodynamics is shown to be based on the same observer-relatedness....

  6. Gravitation, Thermodynamics, and Quantum Theory

    OpenAIRE

    Wald, Robert M.

    1999-01-01

    During the past 30 years, research in general relativity has brought to light strong hints of a very deep and fundamental relationship between gravitation, thermodynamics, and quantum theory. The most striking indication of such a relationship comes from black hole thermodynamics, where it appears that certain laws of black hole mechanics are, in fact, simply the ordinary laws of thermodynamics applied to a system containing a black hole. This article will review the present status of black h...

  7. The Quantum Double in Integrable Quantum Field Theory

    OpenAIRE

    Bernard, D.; Leclair, A.

    1992-01-01

    Various aspects of recent works on affine quantum group symmetry of integrable 2d quantum field theory are reviewed and further clarified. A geometrical meaning is given to the quantum double, and other properties of quantum groups. Multiplicative presentations of the Yangian double are analyzed.

  8. Quantum backreaction in string theory

    International Nuclear Information System (INIS)

    There are situations in string theory when a finite number of string quanta induce a significant backreaction upon the background and render the perturbation theory infrared-divergent. The simplest example is D0-brane recoil under an impact by closed strings. A more physically interesting case is backreaction on the evolution of a totally compact universe due to closed string gas. Such situations necessitate qualitative amendments to the traditional formulation of string theory in a fixed classical background. In this contribution to the proceedings of the XVII European Workshop on String Theory in Padua, I review solved problems and current investigations in relation to this kind of quantum backreaction effects. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  9. Quantum theory can be collectively verified

    OpenAIRE

    Mitra, Arindam

    2009-01-01

    No theory of physics has been collectively scientifically verified in an experiment so far. It is pointed out that probabilistic structure of quantum theory can be collectively scientifically verified in an experiment. It is also argued that experimentalist point of view quantum theory is a complete theory.

  10. Quasi Hopf quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G* as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G* admits a*-operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like Uq(sl2) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G* is canonically associated with Uq(sl2) if qP=-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)

  11. Nekrasov functions from exact Bohr-Sommerfeld periods: the case of SU(N)

    Energy Technology Data Exchange (ETDEWEB)

    Mironov, A [Lebedev Physics Institute, Moscow (Russian Federation); Morozov, A, E-mail: mironov@itep.r, E-mail: mironov@lpi.r, E-mail: morozov@itep.r [ITEP, Moscow (Russian Federation)

    2010-05-14

    We suggested in 2009 that the Nekrasov function with one non-vanishing deformation parameter {epsilon} is obtained by the standard Seiberg-Witten (SW) contour-integral construction. The only difference is that the SW differential pdx is substituted by its quantized version for the corresponding integrable system, and contour integrals become exact monodromies of the wavefunction. This provides an explicit formulation of the earlier guess by Nekrasov and Shatashvili in 2009. In this paper, we successfully check this suggestion in the first order in {epsilon}{sup 2} and the first order in instanton expansion for the SU(N) model, where the consistency of the so-deformed SW equations is already non-trivial.

  12. The Nonlinear Quantum Gauge Theory-Superrelativity

    OpenAIRE

    Leifer, Peter

    1997-01-01

    A new type of a nonlinear gauge quantum theory (superrelativity) has been proposed. Such theory demands a radical reconstruction of both the quantum field conception and spacetime structure, and this paves presumably way to the comprehension of the quantum nature of inertia.

  13. Quantum principal bundles and corresponding gauge theories

    CERN Document Server

    Durdevic, M

    1995-01-01

    A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.

  14. From quantum gravity to quantum field theory via noncommutative geometry

    International Nuclear Information System (INIS)

    A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction, which encodes the kinematics of quantum gravity, we construct semi-classical states which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The emergent interaction involves flux tubes of the gravitational field. In the additional limit, where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. (paper)

  15. A theory of quantum gravity based on quantum computation

    OpenAIRE

    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...

  16. Towards A Theory Of Quantum Computability

    OpenAIRE

    Guerrini, Stefano; Martini, Simone; Masini, Andrea

    2015-01-01

    We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum Turing machine. The class of quantum computable functions is recursively enumerable, thus opening the door to a quantum computability theory which may follow some of the classical developments.

  17. An Introduction to Quantum Game Theory

    CERN Document Server

    Grabbe, J O

    2005-01-01

    This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum mechanical notation and results are introduced as needed. It is also shown that some fundamental problems of quantum mechanics can be formulated as games.

  18. Renormalizable noncommutative quantum field theory

    International Nuclear Information System (INIS)

    We discuss special Euclidean noncommutative φ4-quantum field theory models in two and four dimensions They are examples of renormalizable field theories. Using a Ward identity, it has been shown, that the beta function for the coupling constant vanishes to all orders in perturbation theory. We extend this work and obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. We obtain such relations for the four as well for the two dimensional situation. We expect to learn about renormalisation from this almost solvable models.

  19. Quartic quantum theory: an extension of the standard quantum mechanics

    International Nuclear Information System (INIS)

    We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher-dimensional convex body MNQ of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N-dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N

  20. Quantum Information Theory for Quantum Communication

    Science.gov (United States)

    Koashi, Masato

    This chapter gives a concise description of the fundamental concepts of quantum information and quantum communication, which is pertinent to the discussions in the subsequent chapters. Beginning with the basic set of rules that dictate quantum mechanics, the chapter explains the most general ways to describe quantum states, measurements, and state transformations. Convenient mathematical tools are also presented to provide an intuitive picture of a qubit, which is the simplest unit of quantum information. The chapter then elaborates on the distinction between quantum communication and classical communication, with emphasis on the role of quantum entanglement as a communication resource. Quantum teleportation and dense coding are then explained in the context of optimal resource conversions among quantum channels, classical channels, and entanglement.

  1. Axiomatic quantum field theory in curved spacetime

    CERN Document Server

    Hollands, S

    2008-01-01

    The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and t...

  2. Quantum Theory, namely the pure and reversible theory of information

    CERN Document Server

    Chiribella, G; Perinotti, P

    2012-01-01

    After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental physical theory cannot be described using the ordinary language of Physics? Here we offer a contribution to the problem from the angle of Quantum Information, providing a short non-technical presentation of a recent derivation of Quantum Theory from information-theoretic principles. The broad picture emerging from the principles is that Quantum Theory is the only standard theory of information compatible with the purity and reversibility of physical processes.

  3. Numerical calculations in quantum field theories

    International Nuclear Information System (INIS)

    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

  4. The decoupling approach to quantum information theory

    CERN Document Server

    Dupuis, Frédéric

    2010-01-01

    Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and ha...

  5. Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories

    CERN Document Server

    Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr

    2015-01-01

    We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.

  6. Quantum theory. 2. rev. and enl. ed.

    International Nuclear Information System (INIS)

    This textbook for studyings of physics is oriented in the selection of matter on the contents of a two-semester course about quantum theory. Thereby the foundations of quantum theory, among these the quantum-mechanical measuring process, the mathematical formalism, and Bell's inequalities are extensively treated. Also modern concepts like Feynman's path integral are regarded.The second edition was supplemented by chapters about relativistic quantum mechanics, the quantization of the radiation field, and the spontaneous emission of radiation.

  7. A Topos Theory Foundation for Quantum Mechanics

    OpenAIRE

    Corbett, John V.

    2012-01-01

    The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the standard theory by providing the physical attributes of quantum systems with numerical values that are Dedekind real numbers in the topos of sheaves on the state space of the quantum system. The measured standard real number values of a physical attribute ...

  8. Quantum control theory and applications: A survey

    OpenAIRE

    Dong, Daoyi; Petersen, Ian R.

    2009-01-01

    This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and q...

  9. Quantum Theory of Probability and Decisions

    OpenAIRE

    Deutsch, David

    1999-01-01

    The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory.

  10. Linear response theory for quantum open systems

    OpenAIRE

    J. H. Wei; Yan, YiJing

    2011-01-01

    Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

  11. A first course in topos quantum theory

    International Nuclear Information System (INIS)

    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.

  12. 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.

  13. Quantum theory of human communication

    CERN Document Server

    Slowikowski, W; Slowikowski, Wojtek; Nielsen, Erik B.

    2004-01-01

    We use notions and techniques of Quantum Field Theory to formulate and investigate basic concepts and mechanisms of human communication. We start with attitudes which correspond to photons frequencies, then we introduce states-of-mind which correspond to wave functions. Finally, by way of the second quantization, we come to states-of-opinions which correspond to states of quantized radiation fields. In the present paper we shall only investigate superpositions of pairs of coherent states (e.g. the government and the opposition in a democratic country).

  14. Minimal theory of quantum electrodynamics

    International Nuclear Information System (INIS)

    Within the general framework of the Lehmann-Symanzik-Zimmermann axiomatic field theory, we obtain a simple and coherent formulation of quantum electrodynamics. The definitions of the current densities fulfill the one-particle stability condition, and the commutation relations for the interacting fields are obtained rather than being postulated a priori, thus avoiding the inconsistencies which appear in the canonical formalism. This is possible due to the fact that we use the integral form of the equations of motion in order to compute the propagators and the S matrix. The resulting spectral representations automatically fulfill the correct boundary conditions thus fixing the ubiquitous quasilocal operators in a unique fashion

  15. Introduction to the quantum theory

    CERN Document Server

    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

  16. Quantum field perturbation theory revisited

    Science.gov (United States)

    Matone, Marco

    2016-03-01

    Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.

  17. General relativity, torsion, and quantum theory

    CERN Document Server

    Singh, Tejinder P

    2015-01-01

    We recall some of the obstacles which arise when one tries to reconcile the general theory of relativity with quantum theory. We consider the possibility that gravitation theories which include torsion, and not only curvature, provide better insight into a quantum theory of gravity. We speculate on how the Dirac equation and Einstein gravity could be thought of as limiting cases of a gravitation theory which possesses torsion.

  18. Quantum Hall Physics in String Theory

    OpenAIRE

    Bergman, Oren

    2004-01-01

    In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the corresponding large N matrix model. I review results on the string theory realization of the two-dimensional fractional quantum Hall fluid (FQHF), and describe new results on the stringy description of higher-dimensional analogs.

  19. Localisation in Quantum Field Theory

    CERN Document Server

    Balachandran, A P

    2016-01-01

    In nonrelativistic quantum mechanics , Born's principle of localisation is as follows: For a single particle, if a wave function $\\psi_K$ vanishes outside a spatial region $K$, it is said to be localised in $K$. In particular if a spatial region $K'$ is disjoint from $K$, a wave function $\\psi_{K'}$ localised in $K'$ is orthogonal to $\\psi_K$. Such a principle of localisation does not exist compatibly with relativity and causality in quantum field theory (Newton and Wigner) or interacting point particles (Currie,Jordan and Sudarshan).It is replaced by symplectic localisation of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localisation gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with `continuous' spin. This review outlines the basic principles underlying symplectic localisation and shows or mentions its deep implications. In particular, it has the potential to affect...

  20. Multichannel quantum defect theory: a quantum Poincaré map

    OpenAIRE

    Leyvraz, F.; Méndez-Sánchez, R. A.; Lombardi, M.; Seligman, T. H.

    2000-01-01

    International audience The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincaré map in representation of angular momentum. This has two important implications: we have a paradigm of a true quantum Poincaré map without semi-classical input and we get an entirely new insight into the significance of MQDT.

  1. Learning quantum field theory from elementary quantum mechanics

    International Nuclear Information System (INIS)

    The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem

  2. Fundamental problems in quantum field theory

    CERN Document Server

    Fujita, Takehisa

    2013-01-01

    Quantum physics is based on four fundamental interactions of electromagnetic, weak, gravitational and strong forces. All the interactions are expressed in terms of fermion and boson fields which can describe the quantum states of electrons, nucleons and photons in atoms or nuclei. Correct behaviors of these particles can now be described by the basic field theory terminology, and this textbook explains, for the first time, quantum field theory in a unifying method. At present, modern quantum theory is at a critical junction between different theories, and this textbook presents a clear descrip

  3. Thermodynamics and the structure of quantum theory

    CERN Document Server

    Krumm, Marius; Barrett, Jonathan; Mueller, Markus P

    2016-01-01

    Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Results in quantum gravity and general ideas of what a fundamental theory should look like suggest that thermodynamics plays a major role in the foundations of physics. In this paper, we address the question of which parts of quantum theory are already determined by compatibility with thermodynamics, and which aspects may still admit modification. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechan...

  4. A Quantum Theory of Magnetism

    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.

  5. A Quantum Theory of Magnetism

    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 plausible explanations for the Pauli exclusion principle, Chemical Reactivity and Chemical Bonds. This new interaction has been confirmed by numerical experiments. It establishes magnetism as a force entirely separate from the electromagnetic interaction and converts all of classical magnetism into a quantum theory.

  6. The lesson of quantum theory

    International Nuclear Information System (INIS)

    The concepts of quantal states and complementarity introduced by Niels Bohr in an intuitive though definitive manner more than a generation ago have come to form cornerstones in our description of nature. The Centenary Symposium celebrating Niels Bohr pays tribute to his work which gave birth to contemporary physics and nourished related fields of knowledge. The book is divided into three parts. Part One consists of two communications to the Royal Danish Academy of Sciences and Letters in memory of Niels Bohr. Part Two containing the main theme of the proceedings is divided into three sections. The title of the first, The Lesson of Quantum Theory, is an expression often used by Niels Bohr as time and again he endeavoured an ever deeper analysis of this lesson and its succinct formulation. For Bohr the lesson of quantum theory went beyond physics encompassing not only the natural sciences but all human conceptions. Thus the second section, Unity of Knowledge, conveys the progress in neighbouring disciplines in which Bohr took a particular interest. The last section, Niels Bohr, is dedicated to his personality, his activities, and his world of thought. Part three renders speeches and anecdotes presented during the evening gathering at Ny Carlsberg Glyptoteket on Niels Bohr's one hundredth birthday. (Auth.)

  7. The role of quantum discord in quantum information theory

    International Nuclear Information System (INIS)

    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.

  8. Einstein's strugges with quantum theory a reappraisal

    CERN Document Server

    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...

  9. 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

  10. Quantum entanglement: theory and applications

    International Nuclear Information System (INIS)

    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

  11. Space--Time from Topos Quantum Theory

    Science.gov (United States)

    Flori, Cecilia

    One of the main challenges in theoretical physics in the past 50 years has been to define a theory of quantum gravity, i.e. a theory which consistently combines general relativity and quantum theory in order to define a theory of space-time itself seen as a fluctuating field. As such, a definition of space-time is of paramount importance, but it is precisely the attainment of such a definition which is one of the main stumbling blocks in quantum gravity. One of the striking features of quantum gravity is that although both general relativity and quantum theory treat space-time as a four-dimensional (4D) manifold equipped with a metric, quantum gravity would suggest that, at the microscopic scale, space-time is somewhat discrete. Therefore the continuum structure of space-time suggested by the two main ingredients of quantum gravity seems to be thrown into discussion by quantum gravity itself. This seems quite an odd predicament, but it might suggest that perhaps a different mathematical structure other than a smooth manifold should model space-time. These considerations seem to shed doubts on the use of the continuum in general in a possible theory of quantum gravity. An alternative would be to develop a mathematical formalism for quantum gravity in which no fundamental role is played by the continuum and where a new concept of space-time, not modeled on a differentiable manifold, will emerge. This is precisely one of the aims of the topos theory approach to quantum theory and quantum gravity put forward by Isham, Butterfield, and Doering and subsequently developed by other authors. The aim of this article is to precisely elucidate how such an approach gives rise to a new definition of space-time which might be more appropriate for quantum gravity.

  12. Uncertainty relation revisited from quantum estimation theory

    Energy Technology Data Exchange (ETDEWEB)

    Watanabe, Yu [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Sagawa, Takahiro [Hakubi Center, Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302 (Japan); Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan); Ueda, Masahito [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)

    2011-10-15

    We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.

  13. Mathematical Techniques for Quantum Communication Theory

    OpenAIRE

    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.

  14. Probabilistic and Statistical Aspects of Quantum Theory

    CERN Document Server

    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

  15. Some Issues in Quantum Information Theory

    Institute of Scientific and Technical Information of China (English)

    Run-Yao Duan; Zheng-Feng Ji; Yuan Feng; Ming-Sheng Ying

    2006-01-01

    Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects: discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis,multiple-copy entanglement transformation, and partial entanglement recovery.

  16. Is quantum theory predictably complete?

    International Nuclear Information System (INIS)

    Quantum theory (QT) provides statistical predictions for various physical phenomena. To verify these predictions a considerable amount of data has been accumulated in the 'measurements' performed on the ensembles of identically prepared physical systems or in the repeated 'measurements' on some trapped 'individual physical systems'. The outcomes of these measurements are, in general, some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. More than 70 years ago the claim was made that QT provided the most complete description of 'individual' physical systems and outcomes of the measurements performed on 'individual' physical systems were obtained in an intrinsically random way. Spin polarization correlation experiments (SPCEs), performed to test the validity of Bell inequalities, clearly demonstrated the existence of strong long-range correlations and confirmed that the beams hitting far away detectors somehow preserve the memory of their common source which would be destroyed if the individual counts of far away detectors were purely random. Since the probabilities describe the random experiments and are not the attributes of the 'individual' physical systems, the claim that QT provides a complete description of 'individual' physical systems seems not only unjustified but also misleading and counter productive. In this paper, we point out that we even do not know whether QT is predictably complete because it has not been tested carefully enough. Namely, it was not proven that the time series of existing experimental data did not contain some stochastic fine structures that could have been averaged out by describing them in terms of the empirical probability distributions. In this paper, we advocate various statistical tests that could be used to search for such fine structures in the data and to

  17. Toward a Quantum Theory of Observation

    OpenAIRE

    Zeh, H. D.

    2003-01-01

    The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the introduction of axiomatic observables. The conventional (collapse) and the Everett interpretations of quantum theory may in principle lead to different dynamical consequences. Finally, a formal ensemble description not based on a concept of lacking information is discussed.

  18. Spectral problems from quantum field theory

    OpenAIRE

    Dmitri V. Vassilevich

    2004-01-01

    We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern developments in quantum field theory and strings and show which new spectral and boundary value problems arise.

  19. The conceptual basis of Quantum Field Theory

    NARCIS (Netherlands)

    Hooft, G. 't

    2007-01-01

    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 ingredients f

  20. Operator Deformations in Quantum Measurement Theory

    OpenAIRE

    Andersson, Andreas

    2013-01-01

    We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by unbounded operators) to play a role also in the more general setting.

  1. Zeno's paradox in quantum theory

    International Nuclear Information System (INIS)

    A quantum-theoretic expression is sought for the probability that an unstable particle prepared initially in a well-defined state will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the startling conclusion that an unstable particle which is continuously observed whether it decays will never be found to decay. Since recording the track of an unstable particle (which can be distinguished from its decay products) realizes such continuous observations to a close degree of approximation, the above conclusion poses a paradox which we call Zeno's Paradox in Quantum Theory. Its implications and possible resolutions are briefly discussed. The mathematical transcription of the above-mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. The known ''no-go'' theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under the theorem as a direct corollary

  2. Guide to Mathematical Concepts of Quantum Theory

    OpenAIRE

    Heinosaari, Teiko; Ziman, Mario

    2008-01-01

    Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole pi...

  3. Quantum tunneling and field electron emission theories

    CERN Document Server

    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

  4. Quantum communication, reference frames and gauge theory

    OpenAIRE

    van Enk, S. J.

    2006-01-01

    We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communi...

  5. Quantum communication, reference frames, and gauge theory

    International Nuclear Information System (INIS)

    We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model

  6. Singularities in quantum field theory

    International Nuclear Information System (INIS)

    The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions - they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regluarized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. It is demonstrated that they are associated with certain mathematical difficulties of unregularized theories. Much of the analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. It is argued that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to delta4(x-y). (author)

  7. Quantum field theory for the gifted amateur

    CERN Document Server

    Lancaster, Tom

    2014-01-01

    Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in ...

  8. Processing Information in Quantum Decision Theory

    Directory of Open Access Journals (Sweden)

    Vyacheslav I. Yukalov

    2009-12-01

    Full Text Available A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intended actions. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. The self-consistent procedure of decision making, in the frame of the quantum decision theory, takes into account both the available objective information as well as subjective contextual effects. This quantum approach avoids any paradox typical of classical decision theory. Conditional maximization of entropy, equivalent to the minimization of an information functional, makes it possible to connect the quantum and classical decision theories, showing that the latter is the limit of the former under vanishing interference terms.

  9. A Resource Framework for Quantum Shannon Theory

    CERN Document Server

    Devetak, I; Winter, A

    2005-01-01

    Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional and memoryless. We formalize two principles that have long been tacitly understood. First, we describe how the Church of the larger Hilbert space allows us to move flexibly between states, channels, ensembles and their purifications. Second, we introduce finite and asymptotic (quantum) information processing resources as the basic objects of quantum Shannon theory and recast the protocols used in direct coding theorems as inequalities between resources. We develop the rules of a resource calculus which allows us to manipulate and combine resource inequalities. This framework si...

  10. Guide to mathematical concepts of quantum theory

    International Nuclear Information System (INIS)

    Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)

  11. Quantum theory informational foundations and foils

    CERN Document Server

    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...

  12. Dynamical symmetry breaking in quantum field theories

    CERN Document Server

    Miransky, Vladimir A

    1993-01-01

    The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.

  13. Renormalizable Quantum Gauge Theory of Gravity

    Institute of Scientific and Technical Information of China (English)

    WU Ning

    2002-01-01

    The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.

  14. Quantum gravity from theory to experimental search

    CERN Document Server

    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.

  15. The Impact of Quantum Cosmology on Quantum Field Theory

    OpenAIRE

    Esposito, Giampiero

    1995-01-01

    The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of quantum amplitudes for Euclidean Maxwell theory and linearized gravity. Within the framework of Faddeev-Popov formalism and zeta-function regularization, various choices of mixed boundary conditions lead to a deeper understanding of quantized gauge fields and qua...

  16. Quantum fermions and quantum field theory from classical statistics

    OpenAIRE

    Wetterich, C.

    2012-01-01

    An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schr\\"odinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.

  17. Emergence of classical theories from quantum mechanics

    CERN Document Server

    Hajicek, Petr

    2012-01-01

    Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is ...

  18. Supergeometry in locally covariant quantum field theory

    CERN Document Server

    Hack, Thomas-Paul; Schenkel, Alexander

    2015-01-01

    In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...

  19. Quantum Field Theory in a Semiotic Perspective

    CERN Document Server

    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...

  20. The conceptual framework of quantum field theory

    CERN Document Server

    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...

  1. Quantum Estimation Theory of Error and Disturbance in Quantum Measurement

    OpenAIRE

    Watanabe, Yu; Ueda, Masahito

    2011-01-01

    We formulate the error and disturbance in quantum measurement by invoking quantum estimation theory. The disturbance formulated here characterizes the non-unitary state change caused by the measurement. We prove that the product of the error and disturbance is bounded from below by the commutator of the observables. We also find the attainable bound of the product.

  2. A general theory of quantum relativity

    Science.gov (United States)

    Minic, Djordje; Tze, Chia-Hsiung

    2004-02-01

    The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.

  3. QUANTUM GRAVITY AND YANG-MILLS THEORY

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2014-01-01

    Full Text Available In this paper, we consider Einstein's theory of gravitation in connection with Yang-Mills theory. The model of the metric satisfying the basic requirements of quantum theory is proposed. The mechanism of generation of baryonic matter of dark energy is discussed

  4. Asymptotic theory of quantum statistical inference

    Science.gov (United States)

    Hayashi, Masahito

    Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Stein's lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dénes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramèr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramèr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramèr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramèr-Rao Bound in Pure States Model: Introduction to Part III-- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure

  5. Discrete Quantum Gravity and Quantum Field Theory

    CERN Document Server

    Gudder, Stan

    2016-01-01

    We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space and employing the standard causal order, the histories become causal sets. These causal sets increase in size rapidly and describe an inflationary period for the early universe. We next consider the symmetry group $G$ for the module. We show that $G$ has order 24 and we construct its group table. In a sense $G$ is a discrete approximation to the Lorentz group. However, we note that it contains no boosts and is essentially a rotation group. Unitary representations of $G$ are constructed. The energy-momentum space dual to the discrete module is obtained and a quantum formalism is derived. A discrete Fock space is introduced on this structure and free quantum fields are considered. Finally, we take the first step in a study of interacting quantum fields.

  6. Representation Theory of Algebraic Groups and Quantum Groups

    CERN Document Server

    Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki

    2010-01-01

    Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

  7. Quantum mechanics as a complete physical theory

    CERN Document Server

    Slavnov, D A

    2002-01-01

    We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.

  8. Quantum mechanics as the objective local theory

    CERN Document Server

    Slavnov, D A

    2002-01-01

    In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the postulates are formulated which allow constructing the updated mathematical scheme of quantum mechanics. This scheme incorporates the standard mathematical apparatus of quantum mechanics. Simultaneously, in it there is a mathematical object, which adequately describes individual experiment.

  9. Is quantum theory compatible with special relativity?

    Indian Academy of Sciences (India)

    M Bahrami; A Shafiee; M Saravani; M Golshani

    2013-03-01

    How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.

  10. Quantum to classical transition in quantum field theory

    CERN Document Server

    Lombardo, F C

    1998-01-01

    We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the cri...

  11. Steps in the philosophy of quantum theory

    International Nuclear Information System (INIS)

    1. Interpretation. The Copenhagen Interpretation (CI) is a minimal semantics to quantum theory, expressing what we know at least. It can be extended into a universal Quantum Theory, applied to the observer as well as to the observed object. 2. A Universal Theory as a Philosophical Problem. A circular epistemology is proposed, consisting of non-hierarchical realism, empirism, apriorism and evolutionism, combined in a description of time: past as discrete facts, future as continuous possibilities. 3. Quantum Logic and the Reconstruction of Quantum Theory. Non-distributive logic and Bell's theorem are discussed following Doebner and Luecke. Reconstruction is briefly described. 4. Further Philosophical Questions. Mind-body problem and holism are briefly discussed. (orig.)

  12. Quantum field theory and the standard model

    CERN Document Server

    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...

  13. Mathematical aspects of quantum field theory

    CERN Document Server

    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.

  14. Aspects of Time in Quantum Theory

    CERN Document Server

    Yearsley, James M

    2011-01-01

    We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their definition therefore touches on foundational issues in quantum theory. Various operational approaches to defining time observables have been proposed in the past. Two of the most common are those based on pulsed measurements in the form of strings of projection operators and continuous measurements in the form of complex potentials. One of the major achievements of this thesis is to prove that these two operational approaches are equivalent. However operational approaches are somewhat unsatisfying by themselves. To provide a definition of time observables which is not linked to a particular measurement scheme we employ the decoherent, or consistent, histories approach to quantum theory. We focus on the arrival time, one particular example of a time observable, and we use the relati...

  15. Parameterized quantum field theory without Haag's theorem

    CERN Document Server

    Seidewitz, Ed

    2015-01-01

    Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...

  16. Quantum Measure Theory: A New Interpretation

    CERN Document Server

    Ghazi-Tabatabai, Yousef

    2009-01-01

    Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models lend themselves to a simple interpretation in which a single history (a single element of the sample space) is deemed to be 'real'; we require only that this real history should not be ruled out by the dynamics, the axioms of which ensure that not all histories are precluded. However, applying this interpretation naively to quantum measure theory we can find experimentally realisable systems (notably the Peres-Kochen-Specker system) in which every history is ruled out by the dynamics, challenging us to formulate a deeper realist framework. Our first response is to hold on to our existing interpretative framework and attempt a revision of the dynamics that would reduce quantum measure theory to a classical dynamics. We explore this approach by examining the histories formulation of a stochastic-collapse model on a ...

  17. Quantum field theories on the Lefschetz thimble

    CERN Document Server

    Cristoforetti, M; Mukherjee, A; Scorzato, L

    2013-01-01

    In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.

  18. Quantum theory and the lattice join

    International Nuclear Information System (INIS)

    An informal explanation is presented of Birkhoff's and von Neumann's proposal according to which it is necessary, due to quantum theory, to replace the well-known lattice of properties, which is a heritage from George Boole, by a new quantum lattice of properties mirroring the structure of the Hilbert space. (Z.S.). 4 figs., 12 refs

  19. "Scars" connect classical and quantum theory

    CERN Multimedia

    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).

  20. Nonperturbative Quantum Field Theory in Astrophysics

    OpenAIRE

    Mazur, Dan

    2012-01-01

    The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.

  1. Group Field Theory and Loop Quantum Gravity

    OpenAIRE

    Oriti, D

    2014-01-01

    We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments.

  2. Quantum theory - essential from cosmos to consciousness

    International Nuclear Information System (INIS)

    Quantum theory is the most successful physical theory. About one third of the gross national product in the developed countries results from its applications. But very often quantum theory is still declared as 'crazy' or 'not understandable'. However, quantum theory has a clear mathematical structure that expresses well-known experiences from every day life: A whole is often more than the sum of its parts, and not only the facts also the possibilities can act. If such structures become important then the consequences differ from the models of classical physics which rests on the fundamental differences between matter and motion, material and force, localization and extension, fullness and emptiness. From quantum theory one can learn that all these differences are useful in many cases but are not fundamental. There are equivalences between them, and these can be extended even to the equivalence between matter, energy and abstract quantum information. It is cosmological funded and is denominated as 'Protyposis' to avoid the connotation of information and meaning. Protyposis enables a fundamentally new understanding of matter which can be seen as 'formed', 'condensed' or 'designed' abstract quantum information. One result of the Protyposis is a derivation of Einstein's equations from the abstract quantum information. Another consequence is the ontological reality of the mind and its connection to a brain which can be explained without any dualistic model.

  3. Principle of general covariance and quantum theory

    International Nuclear Information System (INIS)

    The authors emphasise the distinction between formal and operational notions of general covariance. Classical, formal covariance implies operational covariance. This is not true in quantum theory. Two observers may not agree on the results of measurement of a tensorial object like T/sub ik/ (stress tensor) in quantum theory. In particular, one observer might conclude that the measured value is zero while another might attribute non-zero value to it

  4. Geometric continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

  5. Quantum feedback control and classical control theory

    OpenAIRE

    Doherty, Andrew C.; Habib, Salman; Jacobs, Kurt; Mabuchi, Hideo; Tan, Sze M.

    1999-01-01

    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.

  6. High energy approximations in quantum field theory

    International Nuclear Information System (INIS)

    New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given

  7. Quantum theory from the perspective of general probabilistic theories

    OpenAIRE

    Al-Safi, Sabri Walid

    2015-01-01

    This thesis explores various perspectives on quantum phenomena, and how our understanding of these phenomena is informed by the study of general probabilistic theories. Particular attention is given to quantum nonlocality, and its interaction with areas of physical and mathematical interest such as entropy, reversible dynamics, information-based games and the idea of negative probability. We begin with a review of non-signaling distributions and convex operational theories, including ?black b...

  8. The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

    Science.gov (United States)

    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

  9. From Planck's energy quantum to Yukawa's heavy quantum - the development of quantum theory

    International Nuclear Information System (INIS)

    Brief history of quantum theory has been presented in this review. Part 1 deals with the pre-quantum mechanical development (roughly 1900-1925). Part 2 deals with the central discovery of quantum and wave mechanics (roughly 1925-1928), and Part 3 finally gives the essential fundamental applications and extensions of the new atomic theory (roughly 1926-1935)

  10. Cosmological perturbation theory and quantum gravity

    OpenAIRE

    Brunetti, Romeo; Fredenhagen, Klaus; 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 pr...

  11. Cosmological perturbation theory and quantum gravity

    CERN Document Server

    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.

  12. The decoupling approach to quantum information theory

    Science.gov (United States)

    Dupuis, Frédéric

    2010-04-01

    Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.

  13. 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.

  14. The facets of relativistic quantum field theory

    Science.gov (United States)

    Dosch, H. G.; Müller, V. F.

    2011-04-01

    Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.

  15. Mathematical aspects of quantum field theories

    CERN Document Server

    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...

  16. Generalizing Prototype Theory: A Formal Quantum Framework.

    Science.gov (United States)

    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

  17. Quantum stability of chameleon field theories.

    Science.gov (United States)

    Upadhye, Amol; Hu, Wayne; Khoury, Justin

    2012-07-27

    Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073

  18. On The Quantum Theory of Hall Effect

    OpenAIRE

    Ghaboussi, F.

    1996-01-01

    We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical Chern-Simons-part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall-effect is described by a theory which arises as the classical limit of a theory of quantum Hall-effect. The model explai...

  19. 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.

  20. Quantum information theory with Gaussian systems

    International Nuclear Information System (INIS)

    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.)

  1. Quantum coding theory with realistic physical constraints

    CERN Document Server

    Yoshida, Beni

    2010-01-01

    The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.

  2. 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.

  3. 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.)

  4. Random matrix techniques in quantum information theory

    International Nuclear Information System (INIS)

    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

  5. Quantum gravity, effective fields and string theory

    CERN Document Server

    Bjerrum-Bohr, N E J

    2004-01-01

    We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a c...

  6. From Classical to Quantum Shannon Theory

    CERN Document Server

    Wilde, Mark M

    2011-01-01

    The aim of this book is to develop "from the ground up" all of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.

  7. Relativistic Quantum Mechanics and Field Theory

    Science.gov (United States)

    Gross, Franz

    1999-04-01

    An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.

  8. Quantum field theory from classical statistics

    CERN Document Server

    Wetterich, C

    2011-01-01

    An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...

  9. A Quantum field theory of dyons

    CERN Document Server

    Lechner, K

    1999-01-01

    We construct a classical field theory action which upon quantization via thefunctional integral approach, gives rise to a consistent Dirac-stringindependent quantum field theory. The approach entails a systematic derivationof the correlators of all gauge invariant observables, and also of chargeddyonic fields. Manifest SO(2)-duality invariance and Lorentz invariance areensured by the PST-approach.

  10. Quantum theory of laser-stimulated desorption

    Science.gov (United States)

    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.

  11. Algebraic conformal quantum field theory in perspective

    CERN Document Server

    Rehren, Karl-Henning

    2015-01-01

    Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.

  12. Quantum Field Theory in de Sitter spacetime

    CERN Document Server

    So, Ashaq Hussain; Sibuea, Marlina Rosalinda; Akhoon, Shabir Ahmad; Khanday, Bilal Nisar; Majeed, Sajad Ul; Rather, Asloob Ahmad; Nahvi, Ishaq

    2013-01-01

    In this paper we will analyse quantum ?eld theory on de Sitter space- time. We will ?rst analyse a general scalar and vector ?eld theory on de Sitter spacetime. This is done by ?rst calculating these propagators on four-Sphere and then analytically continuing it to de Sitter spacetime.

  13. Particle scattering in nonassociative quantum field theory

    CERN Document Server

    Dzhunushaliev, V D

    1996-01-01

    A model of quantum field theory in which the field operators form a nonassociative algebra is proposed. In such a case, the n-point Green's functions become functionally independent of each other. It is shown that particle interaction in such a theory can be realized by nonlocal virtual objects.

  14. 'Renormalisation infinities' in elementary quantum theory

    International Nuclear Information System (INIS)

    Divergences, closely related to the infinities of relativistic quantum field theory, also occur in non-relativistic single-particle scattering theory. This allows them to be studied in a situation that is unencumbered with other difficulties, and from such a study some insight into both the physics and mathematics of 'renormalisation' can be gained. (author)

  15. Introductory lectures on quantum field theory

    International Nuclear Information System (INIS)

    In these lectures we present a few topics in quantum field theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to particle physics and string theory. (author)

  16. Infrared difficulties with thermal quantum field theories

    International Nuclear Information System (INIS)

    Reviewing briefly the two main difficulties encountered in thermal quantum field theories at finite temperature when dealing with the Braaten-Pisarski (BP) resummation program, the motivation is introduced of an analysis relying on the bare perturbation theory, right from the onset. (author)

  17. Quantum Information Theory and the Foundations of Quantum Mechanics

    CERN Document Server

    Timpson, C G

    2004-01-01

    This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in ...

  18. Dual field theories of quantum computation

    Science.gov (United States)

    Vanchurin, Vitaly

    2016-06-01

    Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus

  19. Introduction to classical and quantum field theory

    International Nuclear Information System (INIS)

    This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)

  20. Quantum field theory in a semiotic perspective

    International Nuclear Information System (INIS)

    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, Poincare, 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 account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)

  1. A heuristic quantum theory of the integer quantum Hall effect

    OpenAIRE

    Kramer, Tobias

    2005-01-01

    Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the quantum current through a Hall device that does not invoke disorder or interactions as the cause of the integer quantum Hall effect (QHE), but is based on a proper quantization of the classical electron drift motion. The theory yields a quantitative descripti...

  2. Quantum simulation of quantum field theory using continuous variables

    Science.gov (United States)

    Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian

    2015-12-01

    The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.

  3. Microscopic theory for quantum mirages in quantum corrals

    OpenAIRE

    Porras Torre, Diego; Fernández Rossier, Joaquín; Tejedor de Paz, Carlos

    2001-01-01

    Scanning tunneling microscopy permits us to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for t...

  4. MATHEMATICAL STRUCTURE OF QUANTUM DECISION THEORY

    OpenAIRE

    Yukalov, Vyacheslav I.; DIDIER SORNETTE

    2010-01-01

    One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision-making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision-...

  5. Processing Information in Quantum Decision Theory

    OpenAIRE

    Yukalov, Vyacheslav I.; Didier Sornette

    2008-01-01

    A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intended actions. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention int...

  6. Clifford algebra in finite quantum field theories

    International Nuclear Information System (INIS)

    We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)

  7. Quantum reality theory and philosophy

    CERN Document Server

    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

  8. Entanglement in non-Hermitian quantum theory

    Indian Academy of Sciences (India)

    Arun K Pati

    2009-09-01

    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 structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet $\\mathcal{PT}$ -symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in $\\mathcal{PT}$ -symmetric quantum theory. Furthermore, we will show how to create entanglement between two $\\mathcal{PT}$ qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.

  9. Emergence of classical theories from quantum mechanics

    International Nuclear Information System (INIS)

    Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

  10. Emergence of classical theories from quantum mechanics

    Science.gov (United States)

    Hájíček, P.

    2012-05-01

    Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

  11. Entanglement in Relativistic Quantum Field Theory

    OpenAIRE

    SHI, YU

    2004-01-01

    I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parameterized either by energy-momentum together with internal degrees of freedom, or by spacetime coordinate together with the component index in the case of a vector or spinor field. In this approach, the notion of entanglement between different spacetime points can be ...

  12. Nondemolition Principle of Quantum Measurement Theory

    OpenAIRE

    Belavkin, V.P.

    2005-01-01

    We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The "collapsed state-vector" after the "objectification" is simply treated as a random vector of the a posteriori state given by the quantum filtering, i.e., the conditioning of the a priori induced state on the corresponding reduced ...

  13. Quantum processes: A Whiteheadian interpretation of quantum field theory

    Science.gov (United States)

    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

  14. Creativity and the Quantum Theory.

    Science.gov (United States)

    Goswami, Amit

    1988-01-01

    The idea that creative acts are quantum jumps in the brain's mechanism is explored. Descriptions of the creative process that support the central role of sudden and discontinuous leaps of thought are cited from various philosophers and scientists. Distinctions between the functions of the brain and of computers are drawn. (VW)

  15. Reasonable fermionic quantum information theories require relativity

    Science.gov (United States)

    Friis, Nicolai

    2016-03-01

    We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.

  16. A Theory of Quantum Space-time

    CERN Document Server

    Francis, C

    1999-01-01

    An empirical re-formulation of modern physics which removes the space-time continuum, and bases physical theory on a small number of rational and empirical principles, thereby removing paradox, eliminating wave particle duality, and restoring reality independent of observation. After briefly describing the philosophical principles underlying the theory, we rigorously construct a discrete model of quantum mechanics. Special relativity is developed through the k-calculus with no manifold. Position is a relationship between particles. Kets are labels which categorise states of matter but do not directly describe them. The principle of superposition is a definitional truism in the categorisation of states. This resolves the measurement problem of quantum mechanics and related paradoxes such as Schrodinger's cat by attributing the collapse of the wave function to information. The probability interpretation has a natural meaning. The model supports a form of relativistic quantum field theory which does not depend o...

  17. Quantum Holonomy Theory and Hilbert Space Representations

    CERN Document Server

    Aastrup, Johannes

    2016-01-01

    We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.

  18. Quantum mechanics of 4-derivative theories

    CERN Document Server

    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.

  19. The physical principles of the quantum theory

    CERN Document Server

    Heisenberg, Werner

    1949-01-01

    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

  20. Remarks on twisted noncommutative quantum field theory

    International Nuclear Information System (INIS)

    We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature. (Orig.)

  1. Quantum mechanics of 4-derivative theories

    International Nuclear Information System (INIS)

    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.)

  2. 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.)

  3. Scattering theory the quantum theory of nonrelativistic collisions

    CERN Document Server

    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

  4. Hilbertian quantum theory as the theory of complementarity

    International Nuclear Information System (INIS)

    It is demonstrated that the notion of complementary physical quantities assumes the possibility of performing ideal first-kind measurements of such quantities. This then leads to an axiomatic reconstruction of the Hilbertian quantum theory based on the complementarity principle and on its connection with the measurement theoretical idealization known as the projection postulate. As the notion of complementary physical quantities does not presuppose the notion of probability, the given axiomatic reconstruction reveals complementarity as an essential reason for the irreducibly probabilistic nature of the quantum theory. (author)

  5. Unstable states in quantum theory

    Science.gov (United States)

    Kuksa, V. I.

    2014-05-01

    Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.

  6. Quantum theory of unambiguous measurements

    CERN Document Server

    Sedlák, Michal

    2010-01-01

    In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification (UI) of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference stat...

  7. Theory of controlled quantum dynamics

    OpenAIRE

    De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio

    1997-01-01

    We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose ...

  8. Undergraduate Lecture Notes in Topological Quantum Field Theory

    OpenAIRE

    Ivancevic, Vladimir G.; Ivancevic, Tijana T.

    2008-01-01

    These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory

  9. Wilson lines in quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.

    2014-07-01

    Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

  10. Wilson lines in quantum field theory

    International Nuclear Information System (INIS)

    Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

  11. Integrable structures in quantum field theory

    Science.gov (United States)

    Negro, Stefano

    2016-08-01

    This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.

  12. 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.)

  13. The Global Approach to Quantum Field Theory

    International Nuclear Information System (INIS)

    Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it is written by a physicist such as Bryce DeWitt, who has made his own contribution to the collection of field theory books with The Global Approach to Quantum Field Theory, all suspicion is naturally abandoned. DeWitt has made a formidable contribution to various areas of physics: general relativity, the interpretation of quantum mechanics, and most of all the quantization of non-Abelian gauge theories and quantum gravity. In addition, his pedagogical publications, especially the Les Houches schools of 1963 and 1983, have had a great impact on quantum field theory. We must begin by alerting the potential readers of this book that it cannot be compared to any other book in the field. This uniqueness applies to both the scientific content and the way the ideas are presented. For DeWitt, a central concept of field theory is that of 'space of histories'. For a field varphii defined on a given spacetime M, the set of all varphii(x) for all x in all charts of M defines its history. It is the space Phi of all possible histories (dynamically allowed or not) of the fields defined on M which is called the 'pace of histories' by DeWitt. If only bosonic fields are considered, the space of histories is an infinite-dimensional manifold and if fermionic fields are also present, it must be viewed as an infinite-dimensional supermanifold. The fields can then be regarded as coordinates on these structures, and the geometrical notions of differentiation, metric, connections, measure, as well as the geodesics which can be defined on it, are of fundamental importance in the development of the formalism of quantum field

  14. Introducing quantum theory a graphic guide

    CERN Document Server

    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.

  15. Towards the mathematics of quantum field theory

    CERN Document Server

    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...

  16. The Operator Tensor Formulation of Quantum Theory

    CERN Document Server

    Hardy, Lucien

    2012-01-01

    A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. We can wire together operations to form circuits. In the standard framework of quantum theory we must foliate the circuit then calculate the probability by evolving a state through it. This approach has three problems. First, we must introduce an arbitrary foliation of the circuit (such foliations are not unique). Second, we have to pad our expressions with identities every time two or more foliation hypersurfaces intersect a given wire. And third, we treat operations corresponding to preparations, transformations, and results in different ways. In this paper we present the operator tensor formulation of quantum theory ...

  17. Canonical Relational Quantum Mechanics from Information Theory

    OpenAIRE

    Munkhammar, Joakim

    2011-01-01

    In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, ...

  18. Multimomentum Hamiltonian Formalism in Quantum Field Theory

    OpenAIRE

    Sardanashvily, G.

    1994-01-01

    The familiar generating functionals in quantum field theory fail to be true measures and, so they make the sense only in the framework of the perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.

  19. GRAVITATIONAL WAVES AND SCHRODINGER QUANTUM THEORY

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2014-02-01

    Full Text Available In this paper, we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation. Conjecture about the Schrödinger wave function due to gravitational waves was proved. Solutions of the gravitational field equations similar to the de Broglie waves have been constructed.

  20. Dual Field Theories of Quantum Computation

    CERN Document Server

    Vanchurin, Vitaly

    2016-01-01

    Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an $N+1$ dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an $N$ dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli $Z$ matrices. Since such situation is not generic we call it the $Z$-problem. On the dual field the...

  1. Quantum theory, deformation and integrability

    CERN Document Server

    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

  2. Theory of controlled quantum dynamics

    International Nuclear Information System (INIS)

    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)

  3. 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)

  4. Theory of controlled quantum dynamics

    CERN Document Server

    De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio

    1997-01-01

    We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.

  5. The Quantum Theory of Magnetism

    CERN Document Server

    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 Green’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.

  6. Non-Equilibrium Time Evolution in Quantum Field Theory

    OpenAIRE

    Wetterich, C.

    1997-01-01

    The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution in non-equilibrium systems.

  7. Introduction to the theory of quantum information processing

    CERN Document Server

    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.

  8. New gravitational forces from quantum theory

    International Nuclear Information System (INIS)

    When a classical theory is quantized, new physical effects result. The prototypical example is the Lamb Shift of quantum electrodynamics. Even though this phenomenon could be parametrized by the ''Uehling Potential,'' it was always realized that it was a quantum aspect of electromagnetism, not a ''new force'' of nature. So, too, with theories of quantum gravity. Generically they predict that there will be spin-1 (graviphoton) and spin-0 (graviscalar) partners of the spin-2 graviton. At some level, these partners will generate new effects. Among them are (1) non-Newtonian gravitational forces and (2) substance dependance (violation of the Principle of Equivalence). We discuss these ideas in the context of recent experiments. (Experiments usually test only one of the above effects, which could be distinct.) We contrast these ideas with the alternative point of view, that there actually may be a ''fifth force'' of nature. 20 refs

  9. How Quantum Theory Helps us Explain

    CERN Document Server

    Healey, Richard

    2011-01-01

    I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: This takes a quantum state to serve solely as a source of sound advice to physically situated agents on the content and appropriate degree of belief about matters concerning which they are currently inevitably ignorant. The general account of how to use quantum states and probabilities to explain otherwise puzzling regularities is then illustrated by showing how we can explain single particle interference phenomena, the stability of matter, and interference of Bose-Einstein condensates. Finally I note some open problems and relate this account to alternative approaches to explanation that emphasize the importance of causation, of unification, and of structure.

  10. Quantum Transport Theory for Photonic Networks

    CERN Document Server

    Lei, Chan U

    2010-01-01

    In this paper, we develop a quantum transport theory to describe photonic transport in photonic networks. The photonic networks concerned in the paper consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The photoncurrents flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The relations between the driven photonic dynamics and photoncurrents are obtained. The quantum dissipation and quantum noise effects in photonic transport are also fully addressed. As an illustration, the theory is applied to the transport phenomena of a driven nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the driven resonator is demonstrated.

  11. A Categorical Framework for Quantum Theory

    CERN Document Server

    Filk, Thomas

    2009-01-01

    Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical 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, in quantum theory the reduction postulate also addresses the "status nascendi" of facts, i.e., their coming into being. Therefore, quantum phyics requires a different conceptual framework which will be elaborated in this article. It is shown that m...

  12. Quantum Lie theory a multilinear approach

    CERN Document Server

    Kharchenko, Vladislav

    2015-01-01

    This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin  Lie algebras;  and Shestakov--Umirbaev  operations for the Lie theory of nonassociative products.  Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.

  13. Neutron Interference Experiments and Quantum Measurement Theory

    Science.gov (United States)

    Namiko, M.; Otake, Y.; Soshi, H.

    1987-03-01

    Physical and epistemological implications of recent experiments on the neutron interference are discussed from the viewpoint of the Machida-Namiki theory of measurement in quantum mechanics, without resort to discussion on the number-phase uncertainty relation. The same idea is also applied to the neutrino oscillation problem.

  14. Quantum theory of two-photon interference

    OpenAIRE

    Wu, Xiang-Yao; Zhang, Bo-Jun; Liu, Xiao-Jing; LI Hong; Zhang, Si-Qi; Jing WANG; Wu, Yi-Heng; Li, Jing-Wu

    2012-01-01

    In this paper, we study two-photon interference with the approach of photon quantum theory, with specific attention to the two-photon interference experiment carried out by Milena D'Angelo et al. (Phys. Rev. Lett 87:013602, 2001). We find the theoretical result is accordance with experiment data.

  15. Quantum kinetic theory of laser plasmas

    International Nuclear Information System (INIS)

    A quantum kinetic equation for plasmas in laser fields is presented. Nonequilibrium properties like the electron-ion collision frequency and collisional absorption are calculated on the basis of a numerical solution of this equation as well as using perturbation theory. (orig.)

  16. Quantum kinetic theory of laser plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Kremp, D.; Bornath, Th.; Bonitz, M. [Rostock Univ. (Germany). Fachbereich Physik; Hilse, P.; Haberland, H.; Schlanges, M. [Greifswald Univ. (Germany). Inst. fuer Physik

    2001-07-01

    A quantum kinetic equation for plasmas in laser fields is presented. Nonequilibrium properties like the electron-ion collision frequency and collisional absorption are calculated on the basis of a numerical solution of this equation as well as using perturbation theory. (orig.)

  17. Wilson lines in quantum field theory

    CERN Document Server

    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.

  18. On Noethers theorem in quantum field theory

    International Nuclear Information System (INIS)

    Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)

  19. Quantum field theory and multiparticle systems

    International Nuclear Information System (INIS)

    The use of quantum field theory methods for the investigation of the physical characteristics of the MANY-BODY SYSTEMS is discussed. Mainly discussed is the method of second quantization and the method of the Green functions. Briefly discussed is the method of calculating the Green functions at finite temperatures. (Z.J.)

  20. Conventions in relativity theory and quantum mechanics

    OpenAIRE

    Svozil, Karl

    2001-01-01

    The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.

  1. Quantum theory of unambiguous measurements

    International Nuclear Information System (INIS)

    In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows use to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference state is the same as the unknown state and the task is to find out unambiguously which one it is. The particular choice of the reference states is unknown to use, and only the probability distribution describing this choice is known. In a general case when multiple copies of unknown and reference states are available I propose a scheme consisting of beam splitters and photodetectors that is optimal within linear optics. Unambiguous identification can be considered as a search in a quantum database, whose elements are the reference states and the query is represented by the unknown state. This perspective motivated me to show that reference states can be recovered after the measurement and might be used (with reduced success rate) in subsequent unambiguous identification. Moreover, I analyze the influence of noise in preparation of coherent states on the performance of the proposed setup. Another problem I address is the unambiguous comparison of a pair of unknown qudit

  2. Unsharp measurements and the conceptual problems of Quantum Theory

    OpenAIRE

    Sturzu, Ioan

    1999-01-01

    The paper emphasis the role of unsharpness in the body of Quantum Theory and the relations to the conceptual problems of the Theory. Key words: quantum measurement, unsharpness, effect, positive operator-valued measure

  3. A Structurally Relativistic Quantum Theory. Part 1: Foundations

    OpenAIRE

    Grgin, Emile

    2012-01-01

    The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A new number system with the properties needed to support an inherently relativistic quantum theory is brought to light and investigated to a point sufficient for applications.

  4. Fundamentals and Prospects of Quantum Field Theories

    International Nuclear Information System (INIS)

    Our present fundamental physics rests on two pillars: Quantum Field Theory and General Relativity. One of the main questions in this area of physics concerns the matching of these two concepts. In addition we hope to improve quantum field theory models by adding gravity effects. Constructive methods led years ago to many beautiful ideas and results, but the main goal to construct a mathematical consistent model of a four-dimensional local quantum field theory, has not been reached. Renormalized perturbation expansions allow to get quantum corrections order by order in a coupling constant. The convergence of this expansion, for example as a Borel summable series, can be questioned, however. In the lectures we first give an introduction to the formulation of local quantum fields within the Minkowski and then within the Euclidean framework. After reviewing the requirements one would like to fulfill, we mention the problems connected with the summability of the renormalized perturbation expansion, which lead to the triviality of the scalar field theory. Phrased differently we address the Landau ghost problem. Subsequently we deal with modifications of the space-time structure leading to new models, which are nonlocal in a particular sense. These models, in general, suffer from the infrared ultraviolet mixing. This can be cured and leads to a special model, which needs 4 (instead of 3) relevant/marginal operators in the defining Lagrangian. This model is renormalizable up to all orders in perturbation theory. In addition a new fixed point appears. In this way, we were able to tame the Landau ghost problem. The renormalization group flow is bounded. We finally discuss Ward identities and Schwinger-Dyson equations. A non-perturbative construction seems to be possible, at least in principle. (author)

  5. Quantum Theory of Laser Amplifiers.

    Science.gov (United States)

    Mander, Gillian Linda

    Available from UMI in association with The British Library. Requires signed TDF. We calculate the input-output characteristics of a below threshold laser amplifier. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions in terms of the corresponding input quantities, and for the photocount first and second factorial moments for both homodyne and direct detection. The general results are applied to several cases of practical interest, including specific non-classical input states. We show that a maximum of twofold amplification is permitted if squeezing in the input is to survive at the output. Similarly, for preservation of photon antibunching in amplification we show that only very small gains are allowed. The model treated here provides a detailed example of the amplifier noise limitations imposed by quantum mechanics. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to the mirror reflectivities. The latter part of this work treats the above threshold laser amplifier. The laser output is back-scattered from a moving target to provide a weak Doppler-shifted signal which re-enters the laser cavity and is amplified. We show that the three-level atomic lasing medium is equivalent to a two-level medium pumped by an inverted bath. We use the methods of quantum statistical analysis to obtain time -evolution equations for the c-number amplitudes of the laser and signal fields. We show that the results may be applied to the below threshold regime for appropriate values of the pump parameter. By considering the amplitude differential gain we show explicitly that the behaviour of the laser around threshold is characteristic of a second -order phase transition. We calculate the output intensity gain appropriate to a heterodyne detection process, and find good agreement between the predicted gain profiles and measured data for both carbon dioxide and argon-ion lasers.

  6. Induced Gravity and Topological Quantum Field Theory

    CERN Document Server

    Oda, Ichiro

    2016-01-01

    We construct an induced gravity (pregeometry) where both the Newton constant and the cosmological constant appear as integration constants in solving field equations. By adding the kinetic terms of ghosts and antighosts, an action of the induced gravity is transformed to a topological field theory. Moreover, by solving field equations of the topological field theory in the FRW universe, we find an inflation solution. The present study might shed some light on a close relationship between the induced gravity and the topological quantum field theory.

  7. Symmetries in perturbative quantum field theory

    International Nuclear Information System (INIS)

    The basic point to be developed in this report amounts to prove that general properties of renormalizable lagrangian field theories can be studied only relying on general theorems of renormalization theory, without any reference to a given renormalization scheme. Moreover, most renormalization problems are thus reduced to purely algebraic ones. The first part of this report is concerned with a general introduction to renormalization theory. General theorems, nammely the quantum action principles, are stated there. In the second part, a few explicit problems are treated in order to exhibit the general techniques needed to get all the results stated in the last part

  8. Quantum geometry and quiver gauge theories

    CERN Document Server

    Nekrasov, Nikita; Shatashvili, Samson

    2013-01-01

    We study macroscopically two dimensional $\\mathcal{N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\\mathbb{T}^{d} \\times \\mathbb{R}^{2}_{\\epsilon}$ of a $d$-dimensional torus and a two dimensional cigar with $\\Omega$-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on $\\mathbb{R}^{2-d} \\times \\mathbb{T}^{2+d}$ and singular monopoles on $\\mathbb{R}^{2-d} \\times \\mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian $\\mathbf{Y}_{\\epsilon}(\\mathfrak{g}_{\\Gamma})$, quantum affine algebra $\\mathbf{U}^{\\mathrm{aff}}_q(\\mathfrak{g}_{\\Gamma})$, or the quantum elliptic algebra $\\mathbf{U}^{\\mathrm{ell}}_{q,p}(\\mathfrak{g}_{\\Gamma})$ associated to Kac-Moody algebra $\\mathfrak{g}_{\\Gamma}$ for quiver $\\Gamma$.

  9. Multiloop Calculations In Perturbative Quantum Field Theory

    CERN Document Server

    Blokland, I R

    2004-01-01

    This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for proble...

  10. Quantum Finite Elements for Lattice Field Theory

    CERN Document Server

    Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan

    2016-01-01

    Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.

  11. Quantum Link Models: A Discrete Approach to Gauge Theories

    OpenAIRE

    Chandrasekharan, S; Wiese, U.-J.

    1996-01-01

    We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed ...

  12. The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory

    OpenAIRE

    Slavnov, D. A.

    2007-01-01

    We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.

  13. Quantum cellular automaton theory of light

    Science.gov (United States)

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-01

    We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.

  14. Spinning Particles in Quantum Mechanics and Quantum Field Theory

    CERN Document Server

    Corradini, Olindo

    2015-01-01

    The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...

  15. Quantum field theory in topology changing spacetimes

    International Nuclear Information System (INIS)

    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.)

  16. Theory of Games on Quantum Objects

    CERN Document Server

    Wu, J

    2005-01-01

    Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players, they are full-structured density matrices with off-diagonal elements for the new games, while reduced diagonal density matrix will be enough for the traditional games on classical objects. In such formalism, the payoff function of every player becomes Hermitian Operator acting on the density matrix. Therefore, the new game looks really like Quantum Mechanics while the traditional game becomes Classical Mechanics.

  17. Heat kernel approach in quantum field theory

    International Nuclear Information System (INIS)

    We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold. We consider both Laplace type operators and non-Laplace type operators on manifolds without boundary as well as Laplace type operators on manifolds with boundary with oblique and non-smooth boundary conditions

  18. Imperfect Cloning Operations in Algebraic Quantum Theory

    Science.gov (United States)

    Kitajima, Yuichiro

    2015-01-01

    No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.

  19. Foundations of quantum theory and thermodynamics

    International Nuclear Information System (INIS)

    Physical reasons to support the statement that Quantum theory (Quantum Gravity in particular as well as Classical Gravity) loose applicability due to Thermodynamical effects are presented. The statement is based on several points: 1. N.Bohr requirement that measuring units must have macro size is one of common fundamentals of Quantum theory. 2. The Reference System--the base notion of Classical and Quantum theory and of any observation process as well, must be protected from any external Thermal influence to provide precise measurements of Time and Distance. 3. No physical screen or process, that can reduce or reflect the action of Gravity is known and hence nothing can cool or protect the measuring units of the Reference System from heating by Thermal Gravity fluctuations. 4. Thermal Gravity fluctuations--Thermal fluctuations of Gravity free fall acceleration, are induced by Thermal behavior of matter and Thermal properties of Electromagnetic fields, but usually are neglected as near zero values. Matter heat Gravity and Gravity heat Matter. Thermal fluctuations of Gravity free fall acceleration act as a Universal Heater on any kind of Matter or Field. 5. Nevertheless the usual Thermal properties of Gravity are negligible, they can be dramatically increased by Gravity Blue Shift (near Gravitational Radius) or usual Doppler effects. 6. If Thermal action of Gravity become significant all measurements of Time and Distance that determine the Reference System notion, must depend on the Thermal properties of Gravity, like Temperature or Entropy, and that violate applicability of the Reference System notion and Quantum and Classical theories as well. If so, Thermal notions, like Temperature or Entropy, become more fundamental than common Time and Distance characters. The definition of the Temperature of the Gravity fluctuations and it's possible measurements are suggested

  20. Theory of quantum error-correcting codes

    International Nuclear Information System (INIS)

    Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. We show that the error for entangled states is bounded linearly by the error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component. copyright 1997 The American Physical Society

  1. Quantum theory of angular momentum

    International Nuclear Information System (INIS)

    This monograph pertains to the angular momentum coupling and recoupling coefficients and their relation to generalized hypergeometric functions; their q-generalization; their polynomial zeros; their relation to orthogonal polynomials; and their numerical computation. The book builds on standard textbook material on Angular Momentum Theory and leads the reader to the recent developments in the selected topics. Fortran programs for the computation of the 3-j, 6-j and 9-j coefficients are included for use by atomic, molecular and nuclear physicists/chemists. (orig.)

  2. Perturbative Quantum Gravity from Gauge Theory

    CERN Document Server

    Bern, Zvi; Johansson, Henrik

    2010-01-01

    In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we suggest that this duality persists to all quantum loop orders and can thus be used to obtain multi-loop gravity amplitudes easily from gauge-theory ones. As a non-trivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.

  3. Renormalization and Interaction in Quantum Field Theory

    International Nuclear Information System (INIS)

    This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory.

  4. Fundamental issues of quantum theory

    CERN Document Server

    Tsai, Yeong-Shyeong

    2008-01-01

    Since the quatum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these concepts, constraints and distribution are ignored in the conventional approach. Further more, there are two versions of quantization relations, one is prior to the field equation and the other is posterior to the field equation. And it is very difficult to find the posterior one. If it is found, of course, these two versions of quantization must be the same one. Actually, it implies that there is recursive problem. In this paper, we will discuss these serious problems.

  5. Observational Consequences of Many-Worlds Quantum Theory

    OpenAIRE

    Page, Don N.

    1999-01-01

    Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur when the number of observers is not uniquely predicted by the theory. In single-history theories, each history is weighted simply by its quantum-mechanical probability, but in many-worlds theories in which random observations are considered, there should a...

  6. Siegert State Approach to Quantum Defect Theory

    CERN Document Server

    Hategan, C; Wolter, H H

    2016-01-01

    The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R- matrix but rather by the equation $1- R_{nn}L_n = 0$, relating R- matrix element $R_{nn}$ to decay channel logarithmic derivative $L_n$. Extension of Siegert state equation to multichannel system results into replacement of channel R- matrix element $R_{nn}$ by its reduced counterpart ${\\cal R}_{nn}$. One proves the Siegert state is a pole, $(1 - {\\cal R}_{nn} L_{n})^{-1}$, of multichannel collision matrix. The Siegert equation $1 - {\\cal R}_{nn} L_{n} = 0$, ($n$ - Rydberg channel), implies basic results of Quantum Defect Theory as Seaton's theorem, complex quantum defect, channel resonances and threshold continuity of averaged multichannel collision matrix elements.

  7. Causal quantum theory and the collapse locality loophole

    International Nuclear Information System (INIS)

    Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no nonlocal correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise definition of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it evident that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments--the collapse locality loophole--which exists because of the possible time lag between a particle entering a measurement device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by ≅0.1 light seconds

  8. Quantum Theories of Self-Localization

    Science.gov (United States)

    Bernstein, Lisa Joan

    In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

  9. A quantum photonic dissipative transport theory

    Science.gov (United States)

    Lei, Chan U.; Zhang, Wei-Min

    2012-05-01

    In this paper, a quantum transport theory for describing photonic dissipative transport dynamics in nanophotonics is developed. The nanophotonic devices concerned in this paper consist of on-chip all-optical integrated circuits incorporating photonic bandgap waveguides and driven resonators embedded in nanostructured photonic crystals. The photonic transport through waveguides is entirely determined from the exact master equation of the driven resonators, which is obtained by explicitly eliminating all the degrees of freedom of the waveguides (treated as reservoirs). Back-reactions from the reservoirs are fully taken into account. The relation between the driven photonic dynamics and photocurrents is obtained explicitly. The non-Markovian memory structure and quantum decoherence dynamics in photonic transport can then be fully addressed. As an illustration, the theory is utilized to study the transport dynamics of a photonic transistor consisting of a nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the external driven field is demonstrated.

  10. A Foundation Theory of Quantum Mechanics

    CERN Document Server

    Mould, R A

    2006-01-01

    The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials, not just to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical obj...

  11. Quantum field theory and Hopf algebra cohomology

    Energy Technology Data Exchange (ETDEWEB)

    Brouder, Christian [Laboratoire de Mineralogie-Cristallographie, CNRS UMR 7590, Universites Paris 6 et 7, IPGP, 4 Place Jussieu, F-75252 Paris Cedex 05 (France); Fauser, Bertfried [Universitaet Konstanz, Fachbereich Physik, Fach M678, D-78457 Konstanz (Germany); Frabetti, Alessandra [Institut Girard Desargues, CNRS UMR 5028, Universite de Lyon 1, 21 av. Claude Bernard, F-69622 Villeurbanne (France); Oeckl, Robert [Centre de Physique Theorique, CNRS UPR 7061, F-13288 Marseille Cedex 9 (France)

    2004-06-04

    We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the sense of Drinfeld. Our approach yields formulae for (perturbative) products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods. Employing Hopf algebra cohomology sheds new light on the structure of QFT and allows the extension to interacting (not necessarily perturbative) QFT. We give a reconstruction theorem for time-ordered products in the spirit of Streater and Wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle. We also demonstrate how non-trivial vacua are described in our approach solving a problem in quantum chemistry.

  12. Bohmian mechanics and quantum theory an appraisal

    CERN Document Server

    Goldstein, Sheldon; Cushing, James T

    1996-01-01

    We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe­ nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's vers...

  13. The coevent formulation of quantum theory

    International Nuclear Information System (INIS)

    Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the existence of zero covers rules out single-history as potential reality (the Kochen Specker theorem casted in histories form is a special case of a zero cover). We see that allowing coarse-grained histories as potential realities avoids the previous paradoxes, maintains deductive non-contextual logic (alas non-Boolean) and gives rise to a unique classical domain. Moreover, we can recover the probabilistic predictions of quantum theory with the use of the Cournot's principle. This formulation, being both a realist formulation and based on histories, is well suited conceptually for the purposes of quantum gravity and cosmology.

  14. Probabilities and signalling in quantum field theory

    OpenAIRE

    Dickinson, Robert; Forshaw, Jeff; Millington, Peter

    2016-01-01

    We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators i...

  15. Entropy and Correlators in Quantum Field Theory

    OpenAIRE

    2010-01-01

    It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the o...

  16. Principle of relativity for quantum theory

    OpenAIRE

    Zaopo, Marco

    2012-01-01

    In non relativistic physics it is assumed that both chronological ordering and causal ordering of events (telling whether there exists a causal relationship between two events or not) are absolute, observer independent properties. In relativistic physics on the other hand chronological ordering depends on the observer who assigns space-time coordinates to physical events and only causal ordering is regarded as an observer independent property. In this paper it is shown that quantum theory can...

  17. Effective quantum field theories in general spacetimes

    OpenAIRE

    Raab, Andreas

    2008-01-01

    We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular reference frames, and the definition is independent of specific background metric and independent of specific regular reference frame. As a consequence, coupling to classical gravity is possible in effective QFTs without getting back-reaction effects. Moreover, w...

  18. Preference reversal in quantum decision theory

    OpenAIRE

    Vyacheslav I. Yukalov; Didier SORNETTE

    2015-01-01

    We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g. for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the ...

  19. Classical solutions in quantum field theories

    International Nuclear Information System (INIS)

    Quantum field theories are difficult to solve because they are governed by nonlinear operator equations. A one-dimensional example, termed the kink, is presented of a classical solution. Topological and nontopological solitons in more than one spatial dimension are also discussed. Euclidean solutions and barrier penetration are also reviewed, focusing on vacuum decay by tunneling, Yang-Mills Instantons, the physical consequences of vacuum tunneling, and thermal fluctuations and sphalerons. 119 refs., 2 figs

  20. Modular forms in quantum field theory

    OpenAIRE

    Brown, Francis; Schnetz, Oliver

    2013-01-01

    The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs up to loop order 10. It is found that many of them are given by Fourier coefficients of modular forms of weights

  1. Quantum Gravity as Theory of "Superfluidity"

    OpenAIRE

    Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

    2005-01-01

    A version of the cosmological perturbation theory in general relativity (GR) is developed, where the cosmological scale factor is identified with spatial averaging of the metric determinant logarithm and the cosmic evolution acquires the pattern of a superfluid motion: the absence of "friction-type" interaction, the London-type wave function, and the Bogoliubov condensation of quantum universes. This identification keeps the number of variables of GR and leads to a new type of potential pertu...

  2. A Categorical Framework for Quantum Theory

    OpenAIRE

    Filk, Thomas; von Mueller, Albrecht

    2009-01-01

    Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical 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...

  3. On the kinetic theory of quantum systems

    International Nuclear Information System (INIS)

    The contents of this thesis which deals with transport phenomena of specific gases, plasmas and fluids, can be separated into two distinct parts. In the first part a statistical way is suggested to estimate the neutrino mass. Herefore use is made of the fact that massive neutrinos possess a non-zero volume viscosity in contrast with massless neutrinos. The second part deals with kinetic theory of strongly condensed quantum systems of which examples in nature are: liquid Helium, heavy nuclei, electrons in a metal and the interior of stars. In degenerate systems fermions in general interact strongly so that ordinary kinetic theory is not directly applicable. For such cases Landau-Fermi-liquid theory, in which the strongly interacting particles are replaced by much weaker interacting quasiparticles, proved to be very useful. A method is developed in this theory to calculate transport coefficients. Applications of this method on liquid 3Helium yield surprisingly good agreement with experimental results for thermal conductivities. (Auth.)

  4. Supersymplectic geometry of supersymmetric quantum field theories

    International Nuclear Information System (INIS)

    We develop a conceptually new, geometric approach to supersymmetry. In particular, we argue that the construction of a generic supersymmetric theory entails only symplectic geometry either in a loop space parameterized by the bosonic degrees of freedom or in a superloop space parameterized by both bosonic and fermionic degrees of freedom. In the bosonic loop space a generic supersymmetric theory can be constructed using a model dependent loop space symplectic two-form, the corresponding symplectic one-form and a model independent vector field that determines circle action in the loop space. In the superloop space the construction of a generic supersymmetric theory employs a model independent symplectic two-form, the pertinent symplectic one-form, a model independent vector field that determines circle action in the superloop space, and the interaction is obtained by introducing a canonical transformation in the superloop space. A Poincare supersymmetric quantum field theory is a realization of our formalism in terms of space-time variables that admit a natural Lorentz-invariant interpretation. We expect that our geometric approach to supersymmetry opens a novel point of view to a large class of problems, including the mechanism of supersymmetry breaking, structure of topological field theories and even aspects of quantum integrability. (orig.)

  5. Realism and Antirealism in Informational Foundations of Quantum Theory

    OpenAIRE

    Tina Bilban

    2014-01-01

    Zeilinger-Brukner's informational foundations of quantum theory, a theory based on Zeilinger's foundational principle for quantum mechanics that an elementary system carried one bit of information, explains seemingly unintuitive quantum behavior with simple theoretical framework. It is based on the notion that distinction between reality and information cannot be made, therefore they are the same. As the critics of informational foundations of quantum theory show, this antirealistic move capt...

  6. Molecular quantum dynamics. From theory to applications

    International Nuclear Information System (INIS)

    calculation of large systems still presents a challenge - despite the considerable power of modern computers - new strategies have been developed to extend the studies to systems of increasing size. Such strategies are presented after a brief overview of the historical background. Strong emphasis is put on an educational presentation of the fundamental concepts, so that the reader can inform himself about the most important concepts, like eigenstates, wave packets, quantum mechanical resonances, entanglement, etc. The chosen examples highlight that high-level experiments and theory need to work closely together. This book thus is a must-read both for researchers working experimentally or theoretically in the concerned fields, and generally for anyone interested in the exciting world of molecular quantum dynamics.

  7. Ultraviolet finite quantum field theory on quantum spacetime

    International Nuclear Information System (INIS)

    We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates qj-qk are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of qj-qk by its expectation value in optimally localized states, while leaving the mean coordinates 1/n(q1 +..+ qn) invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide [9]. Employing an adiabatic switching, we show that the S-matrix is term by term finite. The matrix elements of the transfer matrix are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic limit and the large scale limit of this theory will be studied elsewhere. (orig.)

  8.  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....

  9. Quantum mechanics. A basic course of non-relativistic quantum theory. 2. rev. and upd. ed.

    International Nuclear Information System (INIS)

    The following topics are dealt with: Matter waves and Schroedinger equation, the statistical interpretation of the wave function, uncertainty relations and measuring process, the formal principles of quantum mechanics, angular momentum and particles with spin, perturbation theory and applications, many-electron systems, scattering theory, quantum chemistry, time dependent perturbation theory, fundamental problems of quantum mechanics. (HSI)

  10. Irregular blocks, N = 2 gauge theory and Mathieu system

    Science.gov (United States)

    Piatek, M. R.; Pietrykowski, A. R.

    2016-01-01

    The Alday-Gayotto-Tachikawa (AGT) conjecture relates 4d N = 2, SU(2) SYM theories with Nf matter hypermultiplets to 2d CFT. In case of pure 4d N = 2, SU(2) SYM there is a corresponding irregular conformal block in 2d CFT. The AGT correspondence may be extended within a certain limit (the Nekrasov-Shataschvili limit) to the correspondence between an effective twisted superpotentials of 2d N = 2 SUSY and the Zamolodchikov's “classical” conformal blocks. When narrowed to the pure 4d N = 2 SYM case its limit is related to an irregular classical conformal block. It will be shown that according to the triple correspondence (2dCFT/Gauge/Bethe - c.f. Piatek's talk) the irregular classical conformal block yields spectrum of Mathieu operator. The latter can be obtained as a “classical” limit of the null vector decoupling equation for three-point degenerate irregular block. It will also be shown that the Mathieu spectrum can be also obtained from the limit of the pure gauge theory as a solution of the saddle point equation as well as from the Bohr-Sommerfeld quantization of the Seiberg-Witten theory.

  11. On space of integrable quantum field theories

    CERN Document Server

    Smirnov, F A

    2016-01-01

    We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit...

  12. The Schroedinger equation in quantum field theory

    International Nuclear Information System (INIS)

    Some aspects of the Schroedinger equation in quantum field theory are considered in this article. The emphasis is on the Schroedinger functional equation for Yang-Mills theory, arising mainly out of Feynman's work on (2+1)-dimensional Yang-Mills theory, which he studied with a view to explaining the confinement of gluons. The author extended Feynman's work in two earlier papers, and the present article is partly a review of Feynman's and the author's work and some further extension of the latter. The primary motivation of this article is to suggest that considering the Schroedinger functional equation in the context of Yang-Mills theory may contribute significantly to the solution of the confinement and related problems, an aspect which, in the author's opinion, has not received the attention it deserves. The relation of this problem with certain others such s those of quarks, superconductivity, and quantum gravity is considered briefly, together with certain basic aspects of the formalism that may be interest in their own right, especially for the beginner

  13. A Synopsis of the Minimal Modal Interpretation of Quantum Theory

    OpenAIRE

    Barandes, Jacob A.; Kagan, David

    2014-01-01

    We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite t...

  14. Quantum theory of light double-slit diffraction

    OpenAIRE

    Wu, Xiang-Yao; Li, Hong; Zhang, Bo-Jun; Ma, Ji; Liu, Xiao-Jing; Ba, Nuo; Dong, He; Zhang, Si-Qi; Wang, Jing; Wu, Yi-Heng; Yin, Xin-Guo

    2013-01-01

    In this paper, we study the light double-slit diffraction experiment with quantum theory approach. Firstly, we calculate the light wave function in slits by quantum theory of photon. Secondly, we calculate the diffraction wave function with Kirchhoff's law. Thirdly, we give the diffraction intensity of light double-slit diffraction, which is proportional to the square of diffraction wave function. Finally, we compare calculation result of quantum theory and classical electromagnetic theory wi...

  15. History and future. In commemoration of quantum theory's centenary

    International Nuclear Information System (INIS)

    The history of the discovery of quantum theory and the debate around its interpretation is reviewed. The strong influence of quantum mechanics on the development of science ad philosophy is emphasized and its impact on social technological and economic development is discussed. Possible directions for further development of quantum theory are also mentioned

  16. Weak Quantum Theory: Formal Framework and Selected Applications

    International Nuclear Information System (INIS)

    Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli

  17. Theoretical Physics. Relativistic quantum mechanics, quantum field theory, and elementary-particle theory

    International Nuclear Information System (INIS)

    Of the first in two comprehensive volumes published Theoretical physics of Eckhard Rebhan by this after mechanics, electrodynamics, and quantum mechanics also the relativistic quantum mechanics, the quantum field theory, and the elementary-particle theory are presented in a thinner single volume. The fields treated there will be scarcely required by many physicists in their occupational work. They form however a great achievement of the human mind, of which at least the initial foundations shall belong to the general culture of each interested physicist. Their principal ideas are evident and not more difficultly understandable than the foundations of othe field of physics. In this book it is tried to introduce the reader in large extensiveness so far in the theories, that he should finally be able to study at need more extensive special works.

  18. Strong Dissipative Behavior in Quantum Field Theory

    CERN Document Server

    Berera, A; Ramos, R O; Berera, Arjun; Gleiser, Marcelo; Ramos, Rudnei O.

    1998-01-01

    We study under which conditions an overdamped regime can be attained in the dynamic evolution of a quantum field configuration. Using a real-time formulation of finite temperature field theory, we compute the effective evolution equation of a scalar field configuration, quadratically interacting with a given set of other scalar fields. We then show that, in the overdamped regime, the dissipative kernel in the field equation of motion is closely related to the shear viscosity coefficient, as computed in scalar field theory at finite temperature. The effective dynamics is equivalent to a time-dependent Ginzburg-Landau description of the approach to equilibrium in phenomenological theories of phase transitions. Applications of our results, including a recently proposed inflationary scenario called ``warm inflation'', are discussed.

  19. Measurement theory in local quantum physics

    International Nuclear Information System (INIS)

    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

  20. Measurement theory in local quantum physics

    Science.gov (United States)

    Okamura, Kazuya; Ozawa, Masanao

    2016-01-01

    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.

  1. 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.

  2. Reversible Framework for Quantum Resource Theories.

    Science.gov (United States)

    Brandão, Fernando G S L; Gour, Gilad

    2015-08-14

    In recent years it has been recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This recognition was followed by the development of specific quantum resource theories (QRTs), such as entanglement theory, determining how quantum states that cannot be prepared under certain restrictions may be manipulated and used to circumvent the restrictions. Here we discuss the general structure of QRTs, and show that under a few assumptions (such as convexity of the set of free states), a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotically) a resource. In this case, the asymptotic conversion rate is given in terms of the regularized relative entropy of a resource which is the unique measure or quantifier of the resource in the asymptotic limit of many copies of the state. This measure also equals the smoothed version of the logarithmic robustness of the resource. PMID:26317703

  3. The coevent formulation of quantum theory

    CERN Document Server

    Wallden, Petros

    2013-01-01

    Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the existence of zero covers rules out single-history as potential reality (the Kochen Specker theorem casted in histories form is a special case of a zero cover). We see that allowing coarse-grained histories as potential realities avoids the previous paradoxes, maintains deductive non-contextual logic (alas non-Boolean) and gives rise to a unique classical domain. Moreover, we can recover the probabilistic predictions of quantum theory with the use of the Cournot's principle. This formulation, being both a realist formulation and based on histor...

  4. Quantum field theories of extended objects

    CERN Document Server

    Friedan, Daniel

    2016-01-01

    First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The fields live on the spaces E of relative integral (n-1)-cycles in M -- the integral (n-1)-currents of given boundary. Each E is a complete metric space geometrically analogous to a Riemann surface $\\Sigma$. For example, if $M=S^d$, $\\Sigma = S^2$. The quantum fields on E are to be mapped to observables in a 2d CFT on $\\Sigma$. The correlation functions on E are to be given by the 2d correlation functions on $\\Sigma$. The goal is to construct a CFT of extended objects in d=2n dimensions for every 2d CFT, and eventually a non-conformal QFT of extended objects for every non-conformal 2d QFT, so that all the technology of 2d QFT can be applied to the construction and analysis of quantum field theories of extended objects. The project depends crucially on settling some mathematical q...

  5. Scattering theory for open quantum systems

    International Nuclear Information System (INIS)

    Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator AD in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of AD can be regarded as the Hamiltonian of a closed system which contains the open system {AD,h}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)

  6. Twistor Diagrams and Quantum Field Theory.

    Science.gov (United States)

    O'Donald, Lewis

    Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.

  7. Quantum mechanics in general quantum systems (II): Perturbation theory

    CERN Document Server

    Wang, A M

    2006-01-01

    We propose an improved scheme of perturbation theory based on our exact solution [See: An Min Wang, quant-ph/0611217] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as possible. Our main skills are Hamiltonian redivision so as to overcome a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix product decomposition in order to separate the contraction and anti-contraction terms. Our calculational technology is the limit process for eliminating apparent divergences. Our central idea is ``dynamical rearrangement and summation" for the sake of the partial contributions from the high order even all order approximations absorbed in our perturbed solution. Consequently, we obtain the improved forms of the zeroth, first, second and third order perturbed solutions absorbing the partial contributions from the high order even all order approximations of perturbation. Then we deduce the improved transition probability. In...

  8. Quantum Mind from a Classical Field Theory of the Brain

    OpenAIRE

    Zizzi, Paola

    2011-01-01

    We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzat...

  9. Quantum theory of dispersive electromagnetic modes

    CERN Document Server

    Drummond, P D

    1999-01-01

    A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (plane-wave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group-velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one, two or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (I.R.) and one exciton (U.V.) mode, in order to accurately represent dispersion in transparent solid ...

  10. Preference reversal in quantum decision theory

    CERN Document Server

    Yukalov, V I

    2015-01-01

    We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g. for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the attraction factors entering the expression of quantum probabilities. Only the existence of attraction factors can explain why, considering two lotteries with close utility factors, a decision maker prefers one of them when choosing, but evaluates higher the other one when pricing. We derive a general quantitative criterion for the preference reversal to occur that relates the utilities of the two lotteries to the attraction factors under choosing versus pricing and test successfully its application on experiments by Tvers...

  11. Linear Transformation Theory of Quantum Field Operators and Its Applications

    Institute of Scientific and Technical Information of China (English)

    MA Lei

    2003-01-01

    We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.

  12. Structural aspects of quantum field theory and noncommutative geometry

    CERN Document Server

    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...

  13. Quantum: information theory: technological challenge; Computacion Cuantica: un reto tecnologico

    Energy Technology Data Exchange (ETDEWEB)

    Calixto, M.

    2001-07-01

    The new Quantum Information Theory augurs powerful machines that obey the entangled logic of the subatomic world. Parallelism, entanglement, teleportation, no-cloning and quantum cryptography are typical peculiarities of this novel way of understanding computation. (Author) 24 refs.

  14. A Simple Theory of Quantum Gravity

    CERN Document Server

    Horndeski, Gregory W

    2015-01-01

    A novel theory of Quantum Gravity is presented in which the real gravitons manifest themselves as holes in space. In general, these holes propagate at the speed of light through an expanding universe with boundary denoted by U, which is comprised of pulsating cells. These holes can form bound and semi-bound states. The geometry of U is non-Euclidean on a small scale, but there are indications that it can become Euclidean on a large scale. The motions of elementary particles through U are governed by probability 4 and 7-vectors, which are related to the momentum vectors in Minkowski space. The connection of this theory to Newtonian gravity is discussed, and an expression for the gravitational redshift of photons is derived which relates the redshift to the probability that a photon absorbs a virtual graviton. The theory also provides a possible explanation of dark matter and dark energy as gravitational phenomena, which do not require the introduction of any new particles. A quantum cosmology is presented in w...

  15. The quantum theory of the universe

    International Nuclear Information System (INIS)

    There are two major difficulties with quantizing general relativity: 1. Conceptual difficulty: How can quantum mechanics be applied to the whole universe? What does an observer mean? The observer of the universe cannot be external to the universe, he is a part of the system (the universe) which he observes. 2. Technical problem: The standard perturbation expansion in the gravitational constant produces infinities arising from closed loops. These divergences are not proportional to any terms in the action, and therefore can not be absorbed into coefficients of the terms appearing in the classical action. Quantum gravity is unrenormalizable. There are three known possible solutions to the last problem: 1. A theory in which all the divergences cancel may be found. In N = 8 supergravity, the divergences cancel up to two loops but it is an open question whether or not they cancel in higher orders. 2. The divergences may be due to the use of perturbation theory. Some non-perturbative effects may regularize the divergences at energies above the Planck mass. Personally, I believe that is the correct solution. 3. It may be necessary to add to the action terms with higher than second derivatives, which will make the theory renormalizable. However, this procedure may lead to unitarity violations. For the forthcoming discussion, all three solutions lead to the same type of answer

  16. The Global Approach to Quantum Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Fulling, S A [Texas A and M University (United States)

    2006-05-21

    Parts I and II develop the basic classical and quantum kinematics of fields and other dynamical systems. The presentation is conducted in the utmost generality, allowing for dynamical quantities that may be anticommuting (supernumbers) and theories subject to the most general possible gauge symmetry. The basic ingredients are action functionals and the Peierls bracket, a manifestly covariant replacement for the Poisson bracket and equal-time commutation relations. For DeWitt the logical progression is Peierls bracket {yields} Schwinger action principle {yields} Feynman functional integral although he points out that the historical development was in the opposite order. It must be pointed out that the Peierls-Schwinger-DeWitt approach, despite some advantages over initial-value formulations, has some troubles of its own. In particular, it has never completely escaped from the arena of scattering theory, the paradigm of conventional particle physics. One is naturally led to study matrix elements between an 'in-vacuum' and an 'out-vacuum' though such concepts are murky in situations, such as big bangs and black holes, where the ambient geometry is not asymptotically static in the far past and future. The newest material in the treatise appears in two chapters in part II devoted to the interpretation of quantum theory, incorporating some unpublished work of David Deutsch on the meaning of probability in physics. Parts III through V apply the formalism in depth to successively more difficult classes of systems: quantum mechanics, linear (free) fields, and interacting fields. DeWitt's characteristic tools of effective actions, heat kernels, and ghost fields are developed. Chapters 26 and 31 outline new approaches developed in collaboration with DeWitt's recent students C Molina-Paris and C Y Wang, respectively. The most of parts VI and VII consist of special topics, such as anomalies, particle creation by external fields, Unruh acceleration

  17. Solving UNIQUE-SAT in a Modal Quantum Theory

    CERN Document Server

    Willcock, Jeremiah

    2011-01-01

    In recent work, Benjamin Schumacher and Michael D. Westmoreland investigate a version of quantum mechanics which they call modal quantum theory. This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, modal quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. We show that the problem of UNIQUE-SAT --- which decides whether a given Boolean formula is unsatisfiable or has exactly one satisfying assignment --- is deterministically solvable in any modal quantum theory in constant time. The solution exploits the lack of orthogonality in modal quantum theories and is not ...

  18. Effective equilibrium theory of nonequilibrium quantum transport

    International Nuclear Information System (INIS)

    The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. Here, we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [S. Hershfield, Phys. Rev. Lett. 70 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper, we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field. - Highlights: → Reformulation of steady-state nonequilibrium quantum transport, following Hershfield. → Derivation of effective equilibrium density operator using the 'open-system' approach. → Equivalence with the Keldysh description and formulas relating the two approaches. → Novel framework to treat interactions perturbatively. → Application to nonequilibrium Anderson model and fate of Abrikosov-Suhl resonance.

  19. General System theory, Like-Quantum Semantics and Fuzzy Sets

    OpenAIRE

    Licata, Ignazio

    2007-01-01

    It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics . In conclusion we...

  20. Young's Double Slit Experiment in Quantum Field Theory

    OpenAIRE

    Kenmoku, Masakatsu; Kume, Kenji

    2011-01-01

    Young's double slit experiment is formulated in the framework of canonical quantum field theory in view of the modern quantum optics. We adopt quantum scalar fields instead of quantum electromagnetic fields ignoring the vector freedom in gauge theory. The double slit state is introduced in Fock space corresponding to experimental setup. As observables, expectation values of energy density and positive frequency part of current with respect to the double slit state are calculated which give th...

  1. What information theory can tell us about quantum reality

    OpenAIRE

    Adami, C.; Cerf, N. J.

    1998-01-01

    An investigation of Einstein's ``physical'' reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture base...

  2. A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information

    OpenAIRE

    Plotnitsky, Arkady

    2015-01-01

    This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider H...

  3. Open quantum systems and Random Matrix Theory

    OpenAIRE

    Mulhall, Declan

    2014-01-01

    A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signat...

  4. Entropy and correlators in quantum field theory

    International Nuclear Information System (INIS)

    It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.

  5. Theory of fractional quantum Hall effect

    International Nuclear Information System (INIS)

    A theory of the fractional quantum Hall effect is constructed by introducing 3-particle interactions breaking the symmetry for ν=1/3 according to a degeneracy theorem proved here. An order parameter is introduced and a gap in the single particle spectrum is found. The critical temperature, critical filling number and critical behaviour are determined as well as the Ginzburg-Landau equation coefficients. A first principle calculation of the Hall current is given. 3, 5, 7 electron tunneling and Josephson interference effects are predicted. (author)

  6. On quantum field theory in gravitational background

    International Nuclear Information System (INIS)

    We discuss Quantum Fields on Riemannian space-time. A principle of local definitness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non inertial motion are added. (orig.)

  7. Quantum Electrodynamics Theory of Laser Assisted Recombination

    Institute of Scientific and Technical Information of China (English)

    敖淑艳; 程太旺; 李晓峰; 潘守甫; 傅盘铭

    2003-01-01

    Using a formal scattering theoretical approach, we develop a nonperturbative quantum electrodynamics theory to describe laser assisted recombination (LAR), in which an electron initially in the quantized Volkov state recombines with an ion and emits a high-energy photon with frequency defined by energy conservation laws.The transition probability is expressed as an analytic closed form and the spectrum of LAR reflects mainly the properties of general Bessel functions. For the case of a fast electron the LAR spectrum is confined in a well-defined range, while for a slow electron, the LAR spectrum exhibits a double-plateau structure.

  8. Theory of Quantum Annealing of an Ising Spin Glass

    OpenAIRE

    Santoro, Giuseppe E.; Martonak, Roman; Tosatti, Erio; Car, Roberto

    2002-01-01

    Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random two-dimensional Ising model we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing, based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the re...

  9. Random Matrix Theory and Quantum Chromodynamics

    CERN Document Server

    Akemann, Gernot

    2016-01-01

    These notes are based on the lectures delivered at the Les Houches Summer School in July 2015. They are addressed at a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian Unitary Ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in Quantum Chromodynamics with three colours in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. We also give some ...

  10. Probabilities and Signalling in Quantum Field Theory

    CERN Document Server

    Dickinson, Robert; Millington, Peter

    2016-01-01

    We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.

  11. Nonequilibrium fermion production in quantum field theory

    International Nuclear Information System (INIS)

    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

  12. 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

  13. Gravitational decoherence, alternative quantum theories and semiclassical gravity

    International Nuclear Information System (INIS)

    In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

  14. Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics

    CERN Document Server

    Chen, Yanbei

    2013-01-01

    Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors toward testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this paper, I will review a set of techniques of quantum measurement theory that are often used to analyze quantum optomechanical systems. Some of these techniques were originally designed to analyze how a classical driving force passes through a quantum system, and can eventually be detected with optimal signal-to-noise ratio --- while others focus more on the quantum state evolution of a mechanical object under continuous monitoring. In the second part of this paper, I will review a set of experimental concepts that will demonstrate quantum mechanical behavior of macroscopic objects --- quantum entanglement, quantum teleportation, and the quantum Zeno effect. Taking the interplay between gravity and quan...

  15. A Modern Introduction to Quantum Field Theory

    International Nuclear Information System (INIS)

    This book gives a clear exposition of quantum field theory at the graduate level and the contents could be covered in a two semester course or, with some effort, in a one semester course. The book is well organized, and subtle issues are clearly explained. The margin notes are very useful, and the problems given at the end of each chapter are relevant and help the student gain an insight into the subject. The solutions to these problems are given in chapter 12. Care is taken to keep the numerical factors and notation very clear. Chapter 1 gives a clear overview and typical scales in high energy physics. Chapter 2 presents an excellent account of the Lorentz group and its representation. The decomposition of Lorentz tensors under SO(3) and the subsequent spinorial representations are introduced with clarity. After giving the field representation for scalar, Weyl, Dirac, Majorana and vector fields, the Poincare group is introduced. Representations of 1-particle states using m2 and the Pauli-Lubanski vector, although standard, are treated lucidly. Classical field theory is introduced in chapter 3 and a careful treatment of the Noether theorem and the energy momentum tensor are given. After covering real and complex scalar fields, the author impressively introduces the Dirac spinor via the Weyl spinor; Abelian gauge theory is also introduced. Chapter 4 contains the essentials of free field quantization of real and complex scalar fields, Dirac fields and massless Weyl fields. After a brief discussion of the CPT theorem, the quantization of electromagnetic field is carried out both in radiation gauge and Lorentz gauge. The presentation of the Gupta-Bleuler method is particularly impressive; the margin notes on pages 85, 100 and 101 invaluable. Chapter 5 considers the essentials of perturbation theory. The derivation of the LSZ reduction formula for scalar field theory is clearly expressed. Feynman rules are obtained for the λΦ4 theory in detail and those of QED briefly

  16. Quantum decision theory in simple risky choices

    CERN Document Server

    Favre, M; Heinimann, H R; Yukalov, V I; Sornette, D

    2016-01-01

    Quantum decision theory (QDT) is a novel theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) results, and find that our results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. We examine gender differences in our sample in order to illustrate how QDT can be used to differentiate between ...

  17. Gauge-fields and integrated quantum-classical theory

    International Nuclear Information System (INIS)

    Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs

  18. Multiloop calculations in perturbative quantum field theory

    Science.gov (United States)

    Blokland, Ian Richard

    This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.

  19. Superconformal quantum field theories in string. Gauge theory dualities

    International Nuclear Information System (INIS)

    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.

  20. 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.

  1. The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.

    Science.gov (United States)

    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. PMID:27091170

  2. Foundation of The Two dimensional Quantum Theory of Gravity

    OpenAIRE

    Ghaboussi, F.

    1997-01-01

    The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is shown that the resulting uncertainty relations can explain black hole quantum effects. A quantum gravitational length is also derived which can clarify the origin of Planck length.

  3. Condensates beyond mean field theory: quantum backreaction as decoherence

    OpenAIRE

    Vardi, Amichay; Anglin, James R.

    2000-01-01

    We propose an experiment to measure the slow log(N) convergence to mean-field theory (MFT) around a dynamical instability. Using a density matrix formalism, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break-time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.

  4. Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory

    OpenAIRE

    Marcolli, Matilde; Port, Alexander

    2015-01-01

    Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.

  5. Three Slit Experiments and the Structure of Quantum Theory

    OpenAIRE

    Ududec, Cozmin; Barnum, Howard; Emerson, Joseph

    2009-01-01

    In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin's measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the in...

  6. The effective field theory treatment of quantum gravity

    OpenAIRE

    John F. Donoghue

    2012-01-01

    This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.

  7. Whiteheadian process and quantum theory of mind

    International Nuclear Information System (INIS)

    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 causal connections involving only these things

  8. Continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs

  9. A quantum version of Wigner's transition state theory

    International Nuclear Information System (INIS)

    A quantum version of a recent realization of Wigner's transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in ℎ. This leads to an explicit algorithm to compute cumulative quantum reaction rates and the associated Gamov-Siegert resonances with high accuracy. This algorithm is very efficient since, as opposed to other approaches, it requires no quantum time propagation. This article is based on the presentation by H. Waalkens at the Fifth Workshop on Critical Stability, Erice, Sicily. (author)

  10. Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory

    Science.gov (United States)

    Brunetti, Romeo; Fredenhagen, Klaus; Rejzner, Katarzyna

    2016-08-01

    We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.

  11. What information theory can tell us about quantum reality

    CERN Document Server

    Adami, C

    1998-01-01

    An investigation of Einstein's ``physical'' reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture based on classically accessible observables is, in the worst case of EPR experiments, unrelated to the quantum reality it purports to reflect. Thus, quantum information theory implies that only correlations, not the correlata, are physically accessible: the mantra of the Ithaca interpretation of quantum mechanics.

  12. Recent advances in quantum field theory in curved spacetime

    International Nuclear Information System (INIS)

    A summary is given of several of the current themes of research on quantum field theory in curved spacetime. First, some of the formal issues are reviewed. These include the definitions of quantum states and of path integral measures, and the problems of renormalization. Secondly, several applications of the theory are mentioned. These include curvature dependence of coupling constants, quantum effects near cosmic strings, stability of Kaluza-Klein theories, and quantum fields in de Sitter space. The latter topic is of particular interest because of its importance in inflationary cosmology. (author)

  13. Scaling theory for anomalous semiclassical quantum transport

    International Nuclear Information System (INIS)

    Quantum transport through devices coupled to electron reservoirs can be described in terms of the full counting statistics (FCS) of charge transfer. Transport observables, such as conductance and shot-noise power are just cumulants of FCS and can be obtained from the sample’s average density of transmission eigenvalues, which in turn can be obtained from a finite element representation of the saddle-point equation of the Keldysh (or supersymmetric) nonlinear sigma model, known as quantum circuit theory. Normal universal metallic behavior in the semiclassical regime is controlled by the presence of a Fabry–Pérot singularity in the average density of transmission eigenvalues. We present general conditions for the suppression of Fabry–Pérot modes in the semiclassical regime in a sample of arbitrary shape, a disordered conductor or a network of ballistic quantum dots, which leads to an anomalous metallic phase. Through a double-scaling limit, we derive a scaling equation for anomalous metallic transport, in the form of a nonlinear differential equation, which generalizes the ballistic-diffusive scaling equation of a normal metal. The two-parameter stationary solution of our scaling equation generalizes Dorokhov’s universal single-parameter distribution of transmission eigenvalues. We provide a simple interpretation of the stationary solution using a thermodynamic analogy with a spin-glass system. As an application, we consider a system formed by a diffusive wire coupled via a barrier to normal-superconductor reservoirs. We observe anomalous reflectionless tunneling, when all perfectly transmitting channels are suppressed, which cannot be explained by the usual mechanism of disorder-induced opening of tunneling channels. (paper)

  14. Scaling theory for anomalous semiclassical quantum transport

    Science.gov (United States)

    Sena-Junior, M. I.; Macêdo, A. M. S.

    2016-01-01

    Quantum transport through devices coupled to electron reservoirs can be described in terms of the full counting statistics (FCS) of charge transfer. Transport observables, such as conductance and shot-noise power are just cumulants of FCS and can be obtained from the sample's average density of transmission eigenvalues, which in turn can be obtained from a finite element representation of the saddle-point equation of the Keldysh (or supersymmetric) nonlinear sigma model, known as quantum circuit theory. Normal universal metallic behavior in the semiclassical regime is controlled by the presence of a Fabry-Pérot singularity in the average density of transmission eigenvalues. We present general conditions for the suppression of Fabry-Pérot modes in the semiclassical regime in a sample of arbitrary shape, a disordered conductor or a network of ballistic quantum dots, which leads to an anomalous metallic phase. Through a double-scaling limit, we derive a scaling equation for anomalous metallic transport, in the form of a nonlinear differential equation, which generalizes the ballistic-diffusive scaling equation of a normal metal. The two-parameter stationary solution of our scaling equation generalizes Dorokhov's universal single-parameter distribution of transmission eigenvalues. We provide a simple interpretation of the stationary solution using a thermodynamic analogy with a spin-glass system. As an application, we consider a system formed by a diffusive wire coupled via a barrier to normal-superconductor reservoirs. We observe anomalous reflectionless tunneling, when all perfectly transmitting channels are suppressed, which cannot be explained by the usual mechanism of disorder-induced opening of tunneling channels.

  15. Quantum correlations beyond entanglement and their role in quantum information theory

    CERN Document Server

    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.

  16. Plasmons in QED Vacuum

    CERN Document Server

    Petrov, E Yu

    2016-01-01

    The problem of longitudinal oscillations of an electric field and a charge polarization density in QED vacuum is considered. Within the framework of semiclassical analysis, we calculate time-periodic solutions of bosonized 1+1 dimensional QED (massive Schwinger model). Applying the Bohr--Sommerfeld quantization condition, we determine the mass spectrum of charge-zero bound states (plasmons) which correspond in quantum theory to the found classical solutions. We show that the existence of such plasmons does not contradict any fundamental physical laws and study qualitatively their excitation in 3+1 dimensional real world.

  17. Generalized Schrodinger Equation and Constructions of Quantum Field Theory

    OpenAIRE

    Stoyanovsky, A. V.

    2003-01-01

    The generalized Schrodinger equation deduced in the earlier papers is compared with conventional constructions of quantum field theory. In particular, it yields the usual Schrodinger equation of quantum field theory written without normal ordering. This leads to a definition of certain mathematical version of Feynman integral.

  18. Vacuum energy in some particular quantum field theories

    CERN Document Server

    Jora, Renata

    2016-01-01

    We study the properties of a class of quantum field theories endowed with an equal number of anti commuting and commuting field variables, the most common example being the supersymmetric models. Based on the scaling properties of the partition function we find that these theories have the quantum energy momentum tensor associated to dilatations and thus the vacuum energy equal to zero.

  19. Matrix elements of rq in relativistic quantum defect orbital theory

    International Nuclear Information System (INIS)

    Formulae for the evaluation of the expectation values of rq between the relativistic quantum defect orbital theory wavefunctions are derived. Their recursive structure leads to the development of explicit relations between the formulae for different values of q. The formulae may be considered as a relativistic quantum defect orbital theory generalization of the Kramers' relations for the hydrogenic wavefunctions. (author)

  20. CDT-a entropic theory of quantum gravity

    DEFF Research Database (Denmark)

    Ambjørn, Jan; Görlich, A.; Jurkiewicz, J.;

    2010-01-01

    High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Lattice (hep-lat)......High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Lattice (hep-lat)...

  1. Quantum defect theory and asymptotic methods

    International Nuclear Information System (INIS)

    It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)

  2. Quantum field theory lectures of Sidney Coleman

    CERN Document Server

    Gin-ge Chen, Bryan; Sohn, Richard; Derbes, David

    2016-01-01

    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.

  3. Quantum field theory over F_q

    CERN Document Server

    Schnetz, Oliver

    2009-01-01

    We consider the number \\bar N of points in the projective complement of graph hypersurfaces over F_q. We show that the smallest graphs with non-polynomial \\bar N have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class \\bar N depends on the number of cube roots of unity in F_q. At graphs with 16 edges we find examples where \\bar N can be reduced to the number of points on a (presumably) non-mixed-Tate surface in P^3. In an outlook we show that applying Feynman-rules in F_q lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

  4. Protected gates for topological quantum field theories

    International Nuclear Information System (INIS)

    We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group

  5. Quantum walks and discrete gauge theories

    Science.gov (United States)

    Arnault, Pablo; Debbasch, Fabrice

    2016-05-01

    A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.

  6. Protected gates for topological quantum field theories

    Energy Technology Data Exchange (ETDEWEB)

    Beverland, Michael E.; Pastawski, Fernando; Preskill, John [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Buerschaper, Oliver [Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin (Germany); Koenig, Robert [Institute for Advanced Study and Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Sijher, Sumit [Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)

    2016-02-15

    We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.

  7. The Weinberg - Faddeev solution to the problems of quantum field theory and quantum gravity:quantum spacetime

    OpenAIRE

    Gadiyar, G. H.

    1994-01-01

    In this paper a fundamental length is introduced into physics. This is done in a way which respects special relativity and quantum field theory. The theory has formal similarity to quantum field theory though its properties are far better: divergences are got rid of. The problem of quantizing gravity is straightforward in the approach.

  8. Lectures on algebraic quantum field theory and operator algebras

    International Nuclear Information System (INIS)

    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)

  9. 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)

  10. Optimal Control Theory for Time-Dependent Quantum Transport

    OpenAIRE

    Zhang, Yu

    2015-01-01

    Optical techniques have been employed to coherently control the quantum transport through nanojunctions. Conventional works on optical control of quantum transport usually applied a tailored electrical pulses to perform specific tasks. In this work, an opposite way is employed and a time-dependent driving field is searched to force the system behave in desired pattern. In order to achieve the goal, an optimal control theory for time-dependent quantum transport is developed. The theory provide...

  11. Quantum decoherence in the theory of open systems

    OpenAIRE

    Isar, A.

    2007-01-01

    In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.

  12. Relational modal interpretation for relativistic quantum field theories

    OpenAIRE

    Bene, Gyula

    2001-01-01

    The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for the case of relativistic quantum field theories. Physical systems are defined as Hilbert spaces. The concept of the reduced density matrix is also generalized so that its trace may become smaller than one, expressing the possibility of annihilation. Supers...

  13. Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

    Science.gov (United States)

    Ruggenthaler, Michael; Flick, Johannes; Pellegrini, Camilla; Appel, Heiko; Tokatly, Ilya V.; Rubio, Angel

    2014-07-01

    In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

  14. Towards a Theory of Quantum Black Hole

    OpenAIRE

    Berezin, V.

    2001-01-01

    We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed.

  15. Quantum Theory of Conducting Matter Superconductivity and Quantum Hall Effect

    CERN Document Server

    Fujita, Shigeji; Godoy, Salvador

    2009-01-01

    Explains major superconducting properties including zero resistance, Meissner effect, sharp phase change, flux quantization, excitation energy gap, and Josephson effects using quantum statistical mechanical calculations. This book covers the 2D superconductivity and the quantum Hall effects

  16. Lamb shift in quantum electrodynamics (semiclassical theory)

    International Nuclear Information System (INIS)

    This paper aims to bring some arguments to the proof of the Barut and Van Huele formula, which gives the Lamb shift in the semi-classical theory model: by shortening the calculation owing to the use of a decomposition of the self-potential of the electron; by eliminating the appeal to a divergent series; by bringing justifications and clarifications on some important points of the proof. The effective calculation of the coefficients of the formula is achieved for some of them, and the general analytical form of these coefficients is explicited. It is also proved that the B. and V.H. formula must give results at least as close to the experiment as those of the Bethe formula, which is obtained in Quantum Theory of Fields. Finally one shows that the B. and V.H. formula provides a justification de facto for the cut-off which is used for associating finite numbers to the divergent integrals of the Bethe formula

  17. Bundle Gerbes Applied to Quantum Field Theory

    CERN Document Server

    Carey, A L; Murray, M; Carey, Alan; Mickelsson, Jouko; Murray, Michael

    2000-01-01

    This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and a proof that this leads in a simple manner to the known Schwinger terms (Mickelsson-Faddeev cocycle) for the gauge group action. This gives an explicit computation of the Dixmier-Douady class of the associated bundle gerbe. The method works also in other cases of fermions in external fields (external gravitational field, for example) provided that the APS theorem can be applied; however, we have worked out the details only in the case of vector potentials. Another example, in which the bundle gerbe curvature plays a role, arises from the WZW model on Riemann surfaces. A further example is the `existence of string structures' question. We conclude by showing how global Hamiltonian anomalies fit with...

  18. Quantum mechanics as a theory of probability

    CERN Document Server

    Pitowsky, I

    2005-01-01

    We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only models for the set of axioms are lattices of subspaces of inner product spaces over a field K. (b) Another axiom due to Soler forces K to be the field of real, or complex numbers, or the quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's theorem fully characterizes the probability measures on the algebra of events, so that Born's rule is derived. (d) Gleason's theorem is equivalent to the existence of a certain finite set of rays, with a particular orthogonality graph (Wondergraph). Consequ...

  19. Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

    Science.gov (United States)

    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

  20. Quantum Theory and Human Perception of the Macro-World

    CERN Document Server

    Aerts, Diederik

    2014-01-01

    We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new 'conceptual quantum interpretati...

  1. Resurgence and transseries in quantum theories

    International Nuclear Information System (INIS)

    This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Ecalle resummation. The ideas from QFT use continuity on R1 x S1L, i.e, the absence of any phase transition as N → to infinity, or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical configurations with actions 1/N (kink-instantons), 2/N (bions and bi-kinks), in units where the 2d instanton action is normalized to one. Perturbation theory possesses the IR-renormalon ambiguity that arises due to non-Borel summability of the large-orders perturbation series (of Gevrey-1 type), for which a microscopic cancellation mechanism was unknown. This divergence must be present because the corresponding expansion is on a singular Stokes ray in the complexified coupling constant plane, and the sum exhibits the Stokes phenomenon crossing the ray. We show that there is also a non-perturbative ambiguity inherent to certain neutral topological molecules (neutral bions and bion-anti-bions) in the semiclassical expansion. We find a set of 'confluence equations' that encode the exact cancellation of the two different type of ambiguities. We show that a new notion of 'graded resurgence triangle' is necessary to capture the path integral approach to resurgence, and that graded resurgence underlies a potentially rigorous definition of general QFTs. The mass gap and the Theta angle dependence of vacuum energy are calculated from first principles, and are in accord with large-N and lattice results. (author)

  2. Adiabatic quantum computation and quantum annealing theory and practice

    CERN Document Server

    McGeoch, Catherine C

    2014-01-01

    Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov

  3. Quantum Mechanics as a Theory of Principles, and Beyond

    CERN Document Server

    Minic, D; Minic, Djordje; Tze, Chia-Hsiung

    2003-01-01

    The basic structure of standard quantum mechanics is derived from two compatible postulates. They are: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical. The resulting geometric formulation naturally leads to a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. The basic outcome of such an extension is the interplay between the dynamical metric and symplectic form of the space of quantum events and a dynamical non-integrable almost complex structure. This provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity. The crucial new technical element in our discussion is contained in a set of recent mathematical results concerning the category of infinite dimensional almost Kahler manifolds which replaces the category of complex projective spaces of standard quantum mechanics.

  4. Hierarchical theory of quantum dissipation: Partial fraction decomposition scheme

    OpenAIRE

    Xu, Jian; Xu, Rui-Xue; Luo, Meng; Yan, YiJing

    2009-01-01

    We propose a partial fraction decomposition scheme to the construction of hierarchical equations of motion theory for bosonic quantum dissipation systems. The expansion of Bose--Einstein function in this scheme shows similar properties as it applies for Fermi function. The performance of the resulting quantum dissipation theory is exemplified with spin--boson systems. In all cases we have tested the new theory performs much better, about an order of magnitude faster, than the best available c...

  5. Quantum Theory of Strings in Abelian Higgs Model

    OpenAIRE

    Akhmedov, E. T.; Chernodub, M. N.; Polikarpov, M.I.; Zubkov, M.A.

    1995-01-01

    Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov--Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of th...

  6. Time in quantum mechanics and quantum field theory

    International Nuclear Information System (INIS)

    W Pauli pointed out that the existence of a self-adjoint time operator is incompatible with the semi-bounded character of the Hamiltonian spectrum. As a result, there has been much argument about the time-energy uncertainty relation and other related issues. In this paper, we show a way to overcome Pauli's argument. In order to define a time operator, by treating time and space on an equal footing and extending the usual Hamiltonian H-hat to the generalized Hamiltonian H-hatμ (with H-hat0 = H-hat), we reconstruct the analytical mechanics and the corresponding quantum (field) theories, which are equivalent to the traditional ones. The generalized Schroedinger equation i∂μψ = H-hatμψ and Heisenberg equation d F-hat/dxμ = ∂μ F-hat + i[H-hatμ, F-hat ] are obtained, from which we have: (1) t is to H-hat0 as xj is to H-hatj (j 1, 2, 3); likewise, t is to i∂0 as xj is to i∂j; (2) the proposed time operator is canonically conjugate to i∂0 rather than to H-hat0, therefore Pauli's theorem no longer applies; (3) two types of uncertainty relations, the usual ΔxμΔpμ ≥ 1/2 and the Mandelstam-Tamm treatment ΔxμΔHμ ≥ 1/2, have been formulated

  7. Occupied and unoccupied band structure of Ag(100) determined by photoemission from Ag quantum wells and bulk samples

    International Nuclear Information System (INIS)

    Angle-resolved photoemission spectra taken from atomically uniform films of Ag on Fe(100) show layer-resolved quantum-well peaks. The measured peak positions as a function of film thickness permit a unique determination of the initial band dispersion via the Bohr-Sommerfeld quantization rule. This information, combined with normal-emission data taken from a single crystal Ag(100), leads to a unique determination of the final band dispersion. In this study, we employ a two-band model with four adjustable parameters for a simultaneous fit to these experimental results. The initial and final band dispersions deduced from the fit are accurate to better than 0.03 eV at any wave vector k within the range of measurement. The analytic formula for the band dispersions and the parameters for the best fit are given for future reference. The Fermi wave vector along [100], normalized to the Brillouin-zone size, is determined to be kF/kΓX=0.828±0.001, which is more accurate than the de Haas-van Alphen result. The corresponding Fermi velocity is νF=1.06 in units of the free-electron value. The combined reflection phase for the electron wave at the two boundaries is also deduced and compared with a semiempirical formula. This comparison allows us to deduce the edges of the hybridization gap in the Fe substrate. (c) 2000 The American Physical Society

  8. Quantum Groups and Quantum Field Theory in Rindler Space-Time

    OpenAIRE

    Lambiase, Gaetano

    1996-01-01

    Quantum Field Theory (QFT) developed in Rindler space-time and its thermal properties are analyzed by means of quantum groups approach. The quantum deformation parameter, labelling the unitarily inequivalent representations, turns out to be related to the acceleration of the Rindler frame.

  9. Classical Solutions in Quantum Field Theory

    International Nuclear Information System (INIS)

    Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons-–kinks, vortices, and magnetic monopoles-–and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is

  10. Construction of relativistic quantum theory: a progress report

    International Nuclear Information System (INIS)

    We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact

  11. EDITORIAL: Focus on Quantum Cryptography: Theory and Practice FOCUS ON QUANTUM CRYPTOGRAPHY: THEORY AND PRACTICE

    Science.gov (United States)

    Lütkenhaus, N.; Shields, A. J.

    2009-04-01

    work done to date relates to point-to-point links. Another recent advance has been the development of trusted networks for QKD. This is important for further increasing the range of the technology, and for overcoming denial-of-service attacks on an individual link. It is interesting to see that the optimization of QKD devices differs for point-to-point and network applications. Network operation is essential for widespread adoption of the technology, as it can dramatically reduce the deployment costs and allow connection flexibility. Also important is the multiplexing of the quantum signals with conventional network traffic. For the future, quantum repeaters should be developed for longer range links. On the theoretical side, different approaches to security proofs have recently started to converge, offering several paradigms of the same basic idea. Our improved theoretical understanding places more stringent demands on the QKD devices. We are aware by now that finite size effects in key generation arise not only from parameter estimation. It will not be possible to generate a key from just a few hundred received signals. It is a stimulating challenge for the theory of security proofs to develop lean proof strategies that work with finite signal block sizes. As QKD advances to a real-world cryptographic solution, side channel attacks must be carefully analysed. Theoretical security proofs for QKD schemes are so far based on physical models of these devices. It is in the nature of models that any real implementation will deviate from this model, creating a potential weakness for an eavesdropper to exploit. There are two solutions to this problem: the traditional path of refining the models to reduce the deviations, or the radically different approach of device-independent security proofs, in which none or only a few well controlled assumptions about the devices are made. Clearly, it is desirable to find security proofs that require only minimal or fairly general model

  12. Quantum theory and the role of mind in nature

    CERN Document Server

    Stapp, Henry P

    2001-01-01

    Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort to describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block t...

  13. Deformations of Quantum Field Theories on Curved Spacetimes

    CERN Document Server

    Morales, Eric Morfa

    2012-01-01

    The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and spacelike Killing vector fields carries a family of wedge regions with causal properties analogous to the Minkowski space wedges. Deformations of quantum field theories on these spacetimes are carried out within the operator-algebraic framework - the emerging models share many structural properties with deformations of field theories on flat spacetime. In particular, deformed quantum fields are localized in the wedges of the considered spacetime. As a concrete example, the deformation of the free Dirac field is studied. Second, quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theories turn out to be wedge-local and non-isomorphic to t...

  14. Quantum theory of the solid state part B

    CERN Document Server

    Callaway, Joseph

    1974-01-01

    Quantum Theory of the Solid State, Part B describes the concepts and methods of the central problems of the quantum theory of solids. This book discusses the developed machinery applied to impurities, disordered systems, effects of external fields, transport phenomena, and superconductivity. The representation theory, low field diamagnetic susceptibility, electron-phonon interaction, and Landau theory of fermi liquids are also deliberated. This text concludes with an introduction to many-body theory and some applications. This publication is a suitable textbook for students who have completed

  15. Diffusion, quantum theory, and radically elementary mathematics (MN-47)

    CERN Document Server

    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

  16. Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

    International Nuclear Information System (INIS)

    The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

  17. QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids

    Science.gov (United States)

    Rabani, Eran; Reichman, David R.

    2005-05-01

    We review our recent efforts to formulate and study a mode-coupling approach to real-time dynamic fluctuations in quantum liquids. Comparison is made between the theory and recent neutron scattering experiments performed on liquid ortho-deuterium and para-hydrogen. We discuss extensions of the theory to supercooled and glassy states where quantum fluctuations compete with thermal fluctuations. Experimental scenarios for quantum glassy liquids are briefly discussed.

  18. Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

    Institute of Scientific and Technical Information of China (English)

    QIAN Shang-Wu; GU Zhi-Yu

    2003-01-01

    This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of m≥3 nodes.

  19. Quantum Computation: Theory, Practice, and Future Prospects

    Science.gov (United States)

    Chuang, Isaac

    2000-03-01

    Information is physical, and computation obeys physical laws. Ones and zeros -- elementary classical bits of information -- must be represented in physical media to be stored and processed. Traditionally, these objects are well described by classical physics, but increasingly, as we edge towards the limits of semiconductor technology, we reach a new regime where the laws of quantum physics become dominant. Strange new phenomena, like entanglement and quantum coherence, become available as new resources. How can such resources be utilized for computation? What physical systems allow construction and control of quantum phenomena? How is this relevant to future directions in information technology? The theoretical promise of quantum computation is polynomial speedup of searches, and exponentially speedups for other certain problems such as factoring. But the experimental challenge to realize such algorithms in practice is enormous: to date, quantum computers with only a handful of quantum bits have been realized in the laboratory, using electromagnetically trapped ions, and with magnetic resonance techniques. On the other hand, quantum information has been communicated over long distances using single photons. The future of quantum computation is currently subject to intense scrutiny. It may well be that these machines will not be practical. More quantum algorithms must be discovered, and new physical implementations must be realized. Quantum computation and quantum information are young fields with major issues to be overcome, but already, they have forever changed the way we think of the physical world and what can be computed with it.

  20. Quantum game theory and open access publishing

    Science.gov (United States)

    Hanauske, Matthias; Bernius, Steffen; Dugall, Berndt

    2007-08-01

    The digital revolution of the information age and in particular the sweeping changes of scientific communication brought about by computing and novel communication technology, potentiate global, high grade scientific information for free. The arXiv, for example, is the leading scientific communication platform, mainly for mathematics and physics, where everyone in the world has free access on. While in some scientific disciplines the open access way is successfully realized, other disciplines (e.g. humanities and social sciences) dwell on the traditional path, even though many scientists belonging to these communities approve the open access principle. In this paper we try to explain these different publication patterns by using a game theoretical approach. Based on the assumption, that the main goal of scientists is the maximization of their reputation, we model different possible game settings, namely a zero sum game, the prisoners’ dilemma case and a version of the stag hunt game, that show the dilemma of scientists belonging to “non-open access communities”. From an individual perspective, they have no incentive to deviate from the Nash equilibrium of traditional publishing. By extending the model using the quantum game theory approach it can be shown, that if the strength of entanglement exceeds a certain value, the scientists will overcome the dilemma and terminate to publish only traditionally in all three settings.

  1. The quantum theory of nonlinear optics

    CERN Document Server

    Drummond, Peter D

    2014-01-01

    Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamic...

  2. Some aspects of the theory of quantum groups

    Science.gov (United States)

    Demidov, E. E.

    1993-12-01

    CONTENTSIntroductionChapter I. Basic constructions § 1. Definition of a Hopf algebra § 2. Two constructions of quantum semigroups § 3. Universal coacting and R-matrix algebras § 4. The quantum determinant and antipode § 5. The dimension of quantum semigroupsChapter II. Representation theory § 6. Basic concepts of representation theory § 7. The quantum flag space of \\operatorname{GL}_{P, \\mathcal Q, c}(n) § 8. The Schur algebra and complete reducibility § 9. Representations of \\operatorname{SL}_J(2) §10. The Frobenius morphismChapter III. Non-commutative differential calculus §11. The non-commutative de Rham complex of an n-dimensional vector space §12. Quantum Weyl algebras §13. The de Rham complex of a quantum groupReferences

  3. The Development of Elementary Quantum Theory from 1900 to 1927

    CERN Document Server

    Capellmann, Herbert

    2016-01-01

    Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contri...

  4. The structure of states and maps in quantum theory

    Indian Academy of Sciences (India)

    Sudhavathani Simon; S P Rajagopalan; R Simon

    2009-09-01

    The structure of statistical state spaces in the classical and quantum theories are compared in an interesting and novel manner. Quantum state spaces and maps on them have rich convex structures arising from the superposition principle and consequent entanglement. Communication channels (physical processes) in the quantum scheme of things are in one-to-one correspondence with completely positive maps. Positive maps which are not completely positive do not correspond to physical processes. Nevertheless they prove to be invaluable mathematical tools in establishing or witnessing entanglement of mixed states. We consider some of the recent developments in our understanding of the convex structure of states and maps in quantum theory, particularly in the context of quantum information theory.

  5. Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory

    CERN Document Server

    Dolce, Donatello

    2016-01-01

    In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...

  6. Concepts and methods in the theory of open quantum systems

    OpenAIRE

    Breuer, Heinz-Peter; Petruccione, Francesco

    2003-01-01

    The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate characterization of the quantum statistical ensembles naturally arising in the description of open quantum systems, the corresponding dynamical evolution equations are derived for the Markovian as well as for the non-Markovian case.

  7. Quantum principal bundles and Tannaka-Krein duality theory

    CERN Document Server

    Durdevic, M

    1995-01-01

    The structure of quantum principal bundles is studied, from the viewpoint of Tannaka-Krein duality theory. It is shown that if the structure quantum group is compact, principal G-bundles over a quantum space M are in a natural correspondence with certain contravariant functors defined on the category of finite-dimensional unitary representations of G, with the values in the category of finite projective bimodules over a *-algebra representing the base space.

  8. Quantum Hamilton Mechanics and the Theory of Quantization Conditions

    Science.gov (United States)

    Bracken, Paul

    A formulation of quantum mechanics in terms of complex canonical variables is presented. It is seen that these variables are governed by Hamilton's equations. It is shown that the action variables need to be quantized. By formulating a quantum Hamilton equation for the momentum variable, the energies for two different systems are determined. Quantum canonical transformation theory is introduced and the geometrical significance of a set of generalized quantization conditions which are obtained is discussed.

  9. Perturbation Theory for Quantum Computation with Large Number of Qubits

    OpenAIRE

    Berman, G. P.; Doolen, G. D.; Kamenev, D. I.; Tsifrinovich, V. I.

    2001-01-01

    We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of sc...

  10. Some Thoughts on the Quantum Theory of de Sitter Space

    CERN Document Server

    Banks, T

    2003-01-01

    This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum theory, which can be gleaned from semiclassical considerations. The constraints of a self-consistent measurement theory in such a finite system imply that certain mathematical features of the theory are unmeasurable, and that the theory is consequently mathematically ambiguous. There will be a universality class of mathematical theories all of whose members give the same results for local measurements, within the {\\it a priori} constraints on the precision of those measurements, but make different predictions for unmeasurable quantities, such as the behavior of the system on its Poincare recurrence time scale. A toy model of dS quantum mechanics is presented.

  11. Quantum Theory and Human Perception of the Macro-World

    Directory of Open Access Journals (Sweden)

    Diederik eAerts

    2014-06-01

    Full Text Available We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new `conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing -- light as a geometric theory -- and human touching -- only ruled by Pauli's exclusion principle -- plays a role in our perception of macroscopic entities as ontologically stable objects in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects -- as they occur in smaller entities -- appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping with separated entities, meaning that a more general

  12. Quantum Yang-Mills theory: an overview of a programme

    CERN Document Server

    Milsted, Ashley

    2016-01-01

    We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\\mathbb{Z}/2\\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. ...

  13. Combinatorial Hopf algebras in (noncommutative) quantum field theory

    International Nuclear Information System (INIS)

    We briefly review the role played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.(authors)

  14. Quantum field theory a tourist guide for mathematicians

    CERN Document Server

    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...

  15. Strategic leadership: a view from quantum and chaos theories.

    Science.gov (United States)

    McDaniel, R R

    1997-01-01

    Viewing health care from the perspective of chaos and quantum theories offers new insights into management techniques for effective and efficient delivery of health care services. This article introduces these concepts and gives specific prescriptions for managerial action. PMID:9058085

  16. Aspects of quantum field theory in curved space-time

    CERN Document Server

    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

  17. Grete Hermann: An early contributor to quantum theory

    OpenAIRE

    Herzenberg, C. L.

    2008-01-01

    The life and accomplishments of Grete Hermann are described. During the early twentieth century, she worked in physics, mathematics, philosophy and education. Her most notable accomplishments in physics were in the interpretation of quantum theory.

  18. An algorithm for quaternionic linear equations in quaternionic quantum theory

    International Nuclear Information System (INIS)

    By means of complex representation and companion vector, in this paper we introduce a definition of rank of a quaternion matrix, study the problems of quaternionic linear equations, and obtain an algorithm for quaternionic linear equations in quaternionic quantum theory

  19. Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference

    CERN Document Server

    Bacciagaluppi, G; Bacciagaluppi, Guido; Valentini, Antony

    2006-01-01

    We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive...

  20. A critical note on the greatest days of quantum theory

    International Nuclear Information System (INIS)

    The paper traces the scientific ideas of Louis de Broglie, concerning quantum theory. Uncertainty and scatter; Copenhagen or realism; the argument of Einstein, Podolski and Rosen; and realistic consequences of aspect's experiment; are all discussed. (U.K.)