Showing papers on "Quantization (physics) published in 1985"
Book•
01 Jan 1985TL;DR: Modern Quantum Mechanics as mentioned in this paper is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner, and introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations.
Abstract: Modern Quantum Mechanics is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner. The author, Jun John Sakurai, was a renowned theorist in particle theory. The second edition, revised by Jim Napolitano, introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations, while at the same time retaining classic developments such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequality. A solution manual for instructors using this textbook can be downloaded from www.cambridge.org/9781108422413.
4,221 citations
Book•
01 Jan 1985
TL;DR: In this article, the usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics, and a review on coherent states and some of their applications is given.
Abstract: This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Particular emphasis is given to a general historical introduction, general continuous representations, generalized coherent states, classical and quantum correspondence, path integrals and canonical formalism. Applications are considered in quantum mechanics, optics, quantum chemistry, atomic physics, statistical physics, nuclear physics, particle physics and cosmology. A selection of original papers is reprinted.
1,008 citations
TL;DR: The invariant vacuum state appropriate for inflationary models of the early universe is identified and shown to decay due to the Hawking effect, and a mechanism for dynamically relaxing ..lambda../sub eff/..-->..0 is thereby suggested.
Abstract: In this, the first of a series of papers on quantum field theory in de Sitter spacetime, the invariant vacuum state appropriate for inflationary models of the early universe is identified and shown to decay due to the Hawking effect. The created pairs have an energy-momentum which leads to a first-order decrease of the effective cosmological constant, independently of any matter phase transition. A mechanism for dynamically relaxing ..lambda../sub eff/..-->..0 is thereby suggested.
536 citations
TL;DR: A detailed review of the Starobinsky scenario is given and an observational constraint on the parameters of the model is derived and a cosmological wave function is obtained describing a universe tunneling from ``nothing'' to theStarobinsky inflationary phase.
Abstract: Starobinsky has suggested an inflationary cosmological scenario in which the inflation is driven by quantum corrections to the vacuum Einstein's equations. Here a detailed review of the Starobinsky scenario is given and an observational constraint on the parameters of the model is derived. The quantum mechanics of the model is studied first using the instanton method, and then by solving the corresponding Wheeler-DeWitt equation. A cosmological wave function is obtained describing a universe tunneling from ``nothing'' to the Starobinsky inflationary phase. The curvature fluctuations in the tunneling universe are calculated. This quantum analysis determines the initial conditions for the classical evolution of the model.
384 citations
TL;DR: The first observation of quantized energy levels for a macroscopic variable, namely the phase difference across a current-biased Josephson junction in its zero-voltage state, is reported.
Abstract: We report the first observation of quantized energy levels for a macroscopic variable, namely the phase difference across a current-biased Josephson junction in its zero-voltage state. The position of these energy levels is in quantitative agreement with a quantum mechanical calculation based on parameters of the junction that are measured in the classical regime.
256 citations
TL;DR: In this paper, a manifestly Lorentz covariant formulation of supersymmetric string theory is presented, which constructs the fermion vertex and the supersymmetry generators in a BRST quantization using the techniques of superconformal field theory.
256 citations
TL;DR: Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules, which gives a new insight on the geometry of quantum theory.
Abstract: The generator aspect of observables in classical mechanics leads naturally to a generalized classical mechanics, of which quantum mechanics is shown to be a particular case. Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules. This point of view also gives a new insight on the geometry of quantum theory: Planck's constant is related for instance to the curvature of the quantum-mechanical space of states, and the uniqueness of quantum mechanics can be proved. Finally, the origin of the probabilistic interpretation is discussed.
248 citations
TL;DR: In this paper, the structure of supersymmetric quantum mechanics motivates a modified semiclassical quantization condition for one-dimensional hamiltonians, which gives the exact energy eigenvalues for several potentials for which conventional WKB does not give exact results.
213 citations
TL;DR: In this paper, a mathematical theory of the Laughlin argument for quantization of the Hall conductance for general multiparticle Schrodinger operators with general background potentials is described, which is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class.
Abstract: We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schr\"odinger operators with general background potentials. The quantization is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class. This generalizes ideas of Thouless et al., for noninteracting Bloch Hamiltonians to general (interacting and nonperiodic) ones.
206 citations
TL;DR: In this paper, the generalized Langevin equation and its attendant fluctuation-dissipation relation (FDR) for both classical and quantum systems is explictly derived for a large class of system-bath interaction potentials.
Abstract: The generalized Langevin equation and its attendant fluctuation–dissipation relation (FDR) for both classical and quantum systems is explictly derived for a large class of system‐bath interaction potentials. We demonstrate for this class of potentials that the classical FDR involving only the temperature of the bath is satisfied, and that in general the decay times of the dissipative processes and of the system are temperature dependent. We also demonstrate that the quantum FDR depends in detail on the nature of the bath and on the specific system‐bath interaction. Thus we conclude that while the classical Langevin equation is phenomenologically useful, its quantum counterpart is much more limited.
188 citations
TL;DR: The generalization of the Dirac monopole solution of Maxwell theory to theories of antisymmetric tensor gauge fields of arbitrary rank is considered and a Dirac quantization condition is derived.
Abstract: We consider the generalization of the Dirac monopole solution of Maxwell theory to theories of antisymmetric tensor gauge fields of arbitrary rank. A Dirac quantization condition is derived. These generalized monopoles are expected to be relevant for models of strings and higher-dimensional extended objects, and perhaps also for Kaluza-Klein theories.
TL;DR: In this article, it was shown that in perturbation theoretical calculations the standard Feynman rules remain valid up to a modification of the photon propagator, which allows the explicit calculation of loop diagrams.
TL;DR: A microscopic model of degenerate four-wave mixing including quantization of the medium is given in this paper, where the full effects of loss and spontaneous emission on the squeezing attainable are analyzed.
Abstract: A microscopic model of degenerate four-wave mixing including the quantization of the medium is given. Thus the full effects of loss and spontaneous emission on the squeezing attainable are analyzed. We examine separately the squeezing in the output fields for counterpropagating four-wave mixing, copropagating four-wave mixing, and four-wave mixing in a single-ended optical ring cavity. Good squeezing is possible only in certain limits of atomic parameters.
TL;DR: In the chiral model with three or more flavours, there are topological excitations which can be interpreted as dibaryon states as mentioned in this paper, which correspond to the six-quark states found by Jaffe in the quark model.
TL;DR: In this paper, it was shown that the electron is the seat of an oscillating bound electromagnetic field similar to de Broglie's pilot wave, which is the key to a complete understanding of the Dirac theory of electrons.
Abstract: We explore the possibility thatzitterbewegung is the key to a complete understanding of the Dirac theory of electrons. We note that a literal interpretation of thezitterbewegung implies that the electron is the seat of an oscillating bound electromagnetic field similar to de Broglie's pilot wave. This opens up new possibilities for explaining two major features of quantum mechanics as consequences of an underlying physical mechanism. On this basis, qualitative explanations are given for electron diffraction, the existence of quantized radiationless states, the Pauli principle, and other features of quantum mechanics.
TL;DR: In this article, a variational total energy of the SDW state under the magnetic field is obtained on the basis of the anisotropic two-dimensional Hubbard model, which is in fair agreement with the observed increase of the perpendicular magnetic susceptibility.
Abstract: The energetic gain giving rise to the magnetic-field-induced SDW state in the Bechgaard salts is clarified to originate in the effect of the field to the electronic orbital motion. A variational total energy of the SDW state under the field is obtained on the basis of the anisotropic two-dimensional Hubbard model. Its semi-classical and fully quantum evaluations for the case of the most basic set of the SDW wave vector and the magnetization clearly show a gain of the total energy under the field, which is in fair agreement with the observed increase of the perpendicular magnetic susceptibility. The total energy proves to be lowered by quantization of the closed orbits, since the zero-field state density in the energy region of closed-orbits is a decreasing function of energy. The nature of the successive SDW phase transitions under the field is briefly discussed.
TL;DR: The theory of radiative processes in quantum theory is formulated on the basis of self-energy, in analogy to classical radiation theory, and explicitly carried out for the calculation of the Lamb shift and spontaneous emission.
Abstract: The theory of radiative processes in quantum theory is formulated on the basis of self-energy, in analogy to classical radiation theory, and is explicitly carried out for the calculation of the Lamb shift and spontaneous emission.
Book•
21 Jan 1985
TL;DR: The Breakdown of Classical Mechanics Review of classical mechanics Elementary Systems One-dimensional Problems More One-Dimensional Problems Mathematical Foundations Physical Interpretation Distributions and Fourier Transforms Algebraic Methods Central Force Problems Transformation Theory Non-Degenerate Perturbation Theory Degenerate PERTURBATION Theory Further Approximation Methods Time-Dependent Perturbing Theory Particle in a Uniform Magnetic Field Applications Scattering Theory-Time Dependent Scattering theory-Time Independent Systems of Identical Particles Quantum Statistical Mechanics as mentioned in this paper.
Abstract: The Breakdown of Classical Mechanics Review of Classical Mechanics Elementary Systems One-Dimensional Problems More One-Dimensional Problems Mathematical Foundations Physical Interpretation Distributions and Fourier Transforms Algebraic Methods Central Force Problems Transformation Theory Non-Degenerate Perturbation Theory Degenerate Perturbation Theory Further Approximation Methods Time-Dependent Perturbation Theory Particle in a Uniform Magnetic Field Applications Scattering Theory-Time Dependent Scattering Theory-Time Independent Systems of Identical Particles Quantum Statistical Mechanics.
Book•
31 Dec 1985
TL;DR: In this article, the authors present a generalization of Kroll's procedure for the nonlocal case of the S-Matrix in quantum field theory, and show that it can be used to construct a generalized S-matrix in the non-local case.
Abstract: I: Nonlocal Quantum Field Theory.- I/Foundation of the Nonlocal Model of Quantized Fields.- 1.1. Introduction.- 1.2. Stochastic Space-Time.- 1.3. The Method of Averaging in Stochastic Space-Time and Nonlocality.- 1.4. The Class of Test Functions and Generalized Functions.- 1.4.1. Introduction.- 1.4.2. Space of Test Functions.- 1.4.3. Linear Functional and Generalized Functions.- 1.4.3a. General Definition.- 1.4.3b. Transformation of the Arguments and Differentiation of the Generalized Functions.- 1.4.3c. The Fourier Transform of Generalized Functions.- 1.4.3d. Multiplication of the Generalized Functions by a Smooth Function and Their Convolution.- 1.4.4. Generalized Functions of Quantum Field Theory.- 1.4.5.The Class of Test Functions in the Nonlocal Case.- 1.4.6. The Class of Generalized Functions in the Nonlocal Case.- 2/The Basic Problems of Nonlocal Quantum Field Theory.- 2.1. Nonlocality and the Interaction Lagrangian.- 2.2. Quantization of Nonlocal Field Theory.- 2.2.1. Formulation of the Quantization Problem.- 2.2.2. Regularization Procedure.- 2.2.3. Quantization of the Regularized Equation.- 2.2.4. Green Functions of the Field ??(x).- 2.2.5. The Interacting System Before Removal of the Regularization.- 2.2.6. The Green Functions in the Limit ??0.- 2.3. The Physical Meaning of the Form Factors.- 2.4.The Causality Condition and Unitarity of the S-Matrix in Nonlocal Quantum Field Theory.- 2.4.1. Introduction.- 2.4.2. The Causality Condition.- 2.4.3. The Scheme of Proof of Unitarity of the S-Matrix in Perturbation Theory.- 2.4.4. An Intermediate Regularization Scheme.- 2.4.5. Proof of the Unitarity of the S-Matrix in a Functional Form.- 2.5. The Schroedinger Equation in Quantum Field Theory with Nonlocal Interactions.- 2.5.1. Introduction.- 2.5.2. The Field Operator at Imaginary Time.- 2.5.3. The State Space at Imaginary Time.- 2.5.4. The Interaction Hamiltonian and the Evolution Equation.- 2.5.5. Appendix A.- 3/Electromagnetic Interactions in Stochastic Space-Time.- 3.1. Introduction.- 3.2. Gauge Invariance of the Theory and Generalization of Kroll's Procedure.- 3.3. The Interaction Lagrangian and the Construction of the S-Matrix.- 3.4. Construction of a Perturbation Series for the S-Matrix in Quantum Electrodynamics.- 3.4.1. The Diagrams of Vacuum Polarization.- 3.4.2. The Diagram of Self-Energy.- 3.4.3. The Vertex Diagram and the Corrections to the Anomalous Magnetic Moment (AMM) of Leptons and to the Lamb Shift.- 3.5 The Electrodynamics of Particles with Spins 0 and 1.- 3.5.1. Introduction.- 3.5.2. The Diagrams of the Vacuum Polarization of Boson Fields.- 3.5.3. The Self-Energy of Bosons.- 4/Four-Fermion Weak Interactions in Stochastic Space-Time.- 4.1. Introduction.- 4.2. Gauge Invariance for the S-Matrix in Stochastic-Nonlocal Theory of Weak Interactions.- 4.3. Calculation of the 'Weak' Corrections to the Anomalous Magnetic Moment (AMM) of Leptons.- 4.4. Some Consequences of Neutrino Oscillations in Stochastic- Nonlocal Theory.- 4.4.1. Introduction.- 4.4.2. The $\mu\rightarrow 3e$ Decay.- 4.4.3. The $K_{L}^{0}\rightarrow\mu e$ Decay.- 4.5. Neutrino Electromagnetic Properties in the Stochastic-Nonlocal Theory of Weak Interactions.- 4.6. Studies of the Decay $K_{L}^{0}\rightarrow\mu^{+}\mu^{-}$ and $K_{L}^{0}$- and $K_{S}^{0}$-Meson Mass Difference.- 4.6.1. Introduction.- 4.6.2. The $K_{L}^{0}\rightarrow\mu^{+}\mu^{-}$ Decay.- 4.6.3. The Mass Difference of $K_{L}^{0}$- and $K_{S}^{0}$-Mesons.- 4.7. Appendix B. Calculation of the Contour Integral.- 5/Functional Integral Techniques in Quantum Field Theory.- 5.1. Mathematical Preliminaries.- 5.2. Historical Background of Path Integrals.- 5.3. Analysis on a Finite-Dimensional Grassmann Algebra.- 5.3.1. Definition.- 5.3.2. Derivatives.- 5.3.3. Integration over a Grassmann Algebra (Finite-Dimensional Case).- 5.4. Grassmann Algebra with an Infinite Number of Generators.- 5.4.1. Definition.- 5.4.2. Grassmann Algebra with Involution.- 5.4.3. Functional (or Variational) Derivatives.- 5.4.4. Continual (or Functional) Integrals over the Grassmann Algebra (Formal Definition).- 5.4.5. Examples.- 5.5. Functional Integral and the S-Matrix Theory.- 5.5.1. Introduction.- 5.5.2. Functional Integral over a Bose Field in the Case of Nonlocal-Stochastic Theory (Definition).- 5.5.2a. Definition of Functional Integral.- 5.5.2b. Upper and Lower Bounds of Vacuum Energy E(g) in Nonlocal Theory and in the Anharmonic Oscillator Case.- 5.5.3. Functional Integrals for Fermions in Quantum Field Theory.- II: Stochastic Quantum Mechanics and Fields.- 6/The Basic Concepts of Random Processes and Stochastic Calculus.- 6.1. Events.- 6.2. Probability.- 6.3. Random Variable.- 6.4. Expectation and Concept of Convergence over the Probability.- 6.5. Independence.- 6.6. Conditional Probability and Conditional (Mathematical) Expectation.- 6.7. Martingales.- 6.8. Definition of Random Processes and Gaussian Processes.- 6.9. Stochastic Processes with Independent Increments.- 6.10. Markov Processes.- 6.11. Wiener Processes.- 6.12. Functionals of Stochastic Processes and Stochastic Calculus.- 7/Basic Ideas of Stochastic Quantization.- 7.1. Introduction.- 7.2. The Hypothesis of Space-Time Stochasticity as the Origin of Stochasticity in Physics.- 7.3. Stochastic Space and Random Walk.- 7.4. The Main Prescriptions of Stochastic Quantization.- 7.5. Stochastic Field Theory and its Connection with Euclidean Field Theory.- 7.6. Euclidean Quantum Field Theory.- 8/Stochastic Mechanics.- 8.1. Introduction.- 8.2. Equations of Motion of a Nonrelativistic Particle.- 8.3. Relativistic Dynamics of Stochastic Particles.- 8.4. The Two-Body Problem in Stochastic Theory.- 8.4.1. The Nonrelativistic Case.- 8.4.2. The Relativistic Case.- 9/Selected Topics in Stochastic Mechanics.- 9.1. A Stochastic Derivation of the Sivashinsky Equation for the Self-Turbulent Motion of a Free Particle.- 9.2. Relativistic Feynman-Type Integrals.- 9.2.1. Diffusion Process in Real Time.- 9.2.2. 'Diffusion Process' in Complex Time.- 9.2.3. Introduction of Interactions into the Scheme.- 9.3. Discussion of the Equations of Motion in Stochastic Mechanics.- 9.4. Cauchy Problem for the Diffusion Equation.- 9.5. Position-Momentum Uncertainty Relations in Stochastic Mechanics.- 9.6. Appendix C. Concept of the 'Differential Form' and Directional Derivative.- 10 Further Developments in Stochastic Quantization.- 10.1. Introduction.- 10.2 Davidson's Model for Free Scalar Field Theory.- 10.3. The Electromagnetic Field as a Stochastic Process.- 10.4. Stochastic Quantization of the Gauge Theories.- 10.4.1. Introduction.- 10.4.2. Another Stochastic Quantization Scheme.- 10.5. Equivalence of Stochastic and Canonical Quantization in Perturbation Theory in the Case of Gauge Theories.- 10.6. The Mechanism of the Vacuum Tunneling Phenomena in the Framework of Stochastic Quantization.- 10.7. Stochastic Fluctuations of the Classical Yang-Mills Fields.- 10.8. Appendix D. Solutions to the Free Fokker-Planck Equation.- 11/Some Physical Consequences of the Hypothesis of Stochastic Space-Time and the Fundamental Length.- 11.1. Prologue.- 11.2. Nonlocal-Stochastic Model for Free Scalar Field Theory.- 11.3. Zero-Point Electromagnetic Field and the Connection Between the Value of the Fundamental Length and the Density of Matter.- 11.4. Hierarchical Scales and 'Family' of Black Holes.- 11.5. The Decay of the Proton and the Fundamental Length.- 11.6. A Hypothesis of Nonlocality of Space-Time Metric and its Consequences.- 11.7. On the Origin of Cosmic Rays and the Value of the Fundamental Length.- 11.8. Space-Time Structure near Particles and its Influence on Particle Behavior.- 11.8.1. Introduction.- 11.8.2. Stochastic Behavior of Particles and its Connection with Stochastic Mechanical Dynamics.- 11.8.3. Soliton-Like Behavior of Particles.
TL;DR: In this article, the existence of a non-vanishing 3-cocycle in the unitary, gauge-invariant, ray representations of translations for the quantum mechanics of a charged particle in a background magnetic monopole field was found.
TL;DR: In this paper, the physics of the vacuum as presently understood in quantum field theory is discussed. And heavy reliance is placed on a fundamental analogy between the quantum field and a quantum-mechanical system with (infinitely) many degrees of freedom.
Abstract: In contemporary theories of the structure of matter at very short distance scales, various properties (some of them hypothetical as yet) of the vacuum are of crucial importance. The technical framework for such studies is quantum field theory. The aim of this article is to provide access, for a non-specialist readership, to the physics of the vacuum as presently understood in quantum field theory. To do this, heavy reliance is placed on a fundamental analogy. The basic theoretical entity—the quantum field—is here regarded as analogous to a quantum-mechanical system with (infinitely) many degrees of freedom. A system of interacting quantum fields is then analogous to a complicated system in solid state physics; it can exist in different energy states, namely the ground state and various excited states. The excited states of the field system are characterized by the presence of excitation quanta, which are the particles (electrons, quarks, photons…) of which our material world is composed. In the g...
TL;DR: A modification of the action of Brink and Schwarz (1981) for a particle with spacetime supersymmetry allows quantisation in a Lorentz-covariant gauge as mentioned in this paper.
Abstract: A modification of the action of Brink and Schwarz (1981) for a particle with spacetime supersymmetry allows quantisation in a Lorentz-covariant gauge, defines the usual supersymmetry-covariant derivatives, and implies equations of motion which hold for all massless representations of supersymmetry.
TL;DR: In this article, Hartree and Hartree-Fock proposed the Hartree potential, which is an extension of the Schrodinger Equation of the Green's Function, and showed that it can be used to approximate a wave.
Abstract: 1. The Interacting System.- 1.1. The Basic Problem.- 1.2. The Jellium Solid.- 1.3. Hartree Theory-The Sommerfeld Model.- 1.4. Hartree-Fock.- 1.5. Exchange and Correlation Holes.- 1.6. Correlation Effects and the Thomas-Fermi Model.- Problems.- 2. Green's Functions of the Single-Particle Schrodinger Equation.- 2.1. Green's Functions of the Schrodinger Equation.- 2.2. Green's Functions and Perturbation Theory.- 2.3. Time-Dependent Green's Functions.- 2.4. Green's Function Diagrams.- 2.5. Green's Functions or Wave Functions?.- Problems.- 3. Quantization of Waves (Second Quantization).- 3.1. Waves and Particles.- 3.2. The Linear Chain of Atoms.- 3.3. The General Quantization of a Wave System.- 3.4. Quantization of the Electromagnetic Field.- 3.5. Elementary Excitations and "Particles".- 3.6. Perturbations and the Elementary Excitations.- 3.7. Summary.- Problems.- 4. Representations of Quantum Mechanics.- 4.1. Schrodinger Representation.- 4.2. Heisenberg Representation.- 4.3. Interaction Representation.- 4.4. Occupation Number Representation.- 4.5. Interaction between Waves and Particles.- 4.6. Field Operators.- Problems.- 5. Interacting Systems and Quasiparticles.- 5.1. Single-Particle States.- 5.2. Absorbing Media.- 5.3. Exact and Approximate Eigenstates.- 5.4. Landau Quasiparticles.- Problems.- 6. Many-Body Green's Functions.- 6.1. Definition of the Many-Body Green's Function.- 6.2. Relationship to Single-Particle Green's Function.- 6.3. Energy Structure and the Green's Function.- 6.4. The Lehman Representation and Quasiparticles.- 6.5. Expectation Values.- 6.6. Equation of Motion for the Green's Function.- 6.7. Hartree and Hartree-Fock Approximations.- 6.8. The Self-Energy.- Problems.- 7. The Self-Energy and Perturbation Series.- 7.1. Functional Derivatives and the Calculation of G and ?.- 7.2. Iterative Solution for the Green's Function and Self-Energy.- 7.3. Screening and the Perturbation Series.- 7.4. The Screened Interaction and Selective Summations.- 7.5. The Uniform System.- Problems.- 8. Diagrammatic Interpretation of the Green's Function Series.- 8.1. Diagrammatic Interpretation of the Perturbation Series.- 8.2. Diagrammatic Expansion.- 8.3. Infinite Series and Irreducible Diagrams.- 8.4. The Hartree Potential.- 8.5. The Uniform System.- 8.6. Rules for Evaluating Diagrams.- 8.7. Selective Summations.- 8.8. Practical Aspects of Diagrammatics.- Problems.- 9. The Normal System.- 9.1. The Jellium Solid Response Function.- 9.2. The Self-Energy (Physical Considerations).- 9.3. Evaluation of the Self-Energy and Quasiparticle Properties.- 9.4. Landau Quasiparticles.- 9.5. Insulating Systems.- 9.6. Surfaces.- Problems.- 10. Thermal Effects on the Green's Function.- 10.1. The Density Matrix.- 10.2. Statistical Mechanics.- 10.3. The "Thermal" Heisenberg Representation.- 10.4. Evaluation of the Perturbation Expansion.- 10.5. Periodicity of G and the Extension to Energy Dependency.- 10.6. Real-Time Thermal Green's Functions.- Problems.- 11. Boson Particles.- 11.1. Collective Excitations in Solids.- 11.2. Electron-Phonon System.- 11.3. Plasmons and the Total Interaction.- 11.4. Boson Systems with a Condensate.- Problems.- 12. Special Methods.- 12.1. The Density Functional Method (Nearly Uniform Electron Gases).- 12.2. Highly Localized Systems (Anderson-Hubbard Models).- 12.3. Canonical Transformations.- 12.4. Mean-Field Theory.- Problems.- 13. Superconductivity.- 13.1. Cooper Pairs.- 13.2. Canonical Transformations.- 13.3. Propagator Approach.- Problems.- Appendix: List of Symbols.
TL;DR: In the limit that the scale factor vanishes the presence of the massive scalar field does not result in any new types of solutions, nor does it eliminate any, so the results of the first paper of this series on the existence of particle horizons are also valid for solutions beginning with zero scale factor if a conformally coupled massive scaler field is present.
Abstract: The behaviors of solutions to the semiclassical backreaction equations are investigated for conformally invariant free quantum fields and a conformally coupled massive scalar field in spatially flat homogeneous and isotropic spacetimes containing classical radiation. With one exception, only solutions that begin with the scale factor equal to zero are considered. It is found that in the limit that the scale factor vanishes the presence of the massive scalar field does not result in any new types of solutions, nor does it eliminate any. Thus the results of the first paper of this series on the existence of particle horizons are also valid for solutions beginning with zero scale factor if a conformally coupled massive scalar field is present. For intermediate values of the scale factor the massive scalar field can significantly affect the behaviors of specific solutions. Nevertheless, no new types of behaviors are observed and no old ones are eliminated. For large values of the scale factor it is uncertain what the behaviors of all solutions are, but asymptotically de Sitter solutions and asymptotically classical solutions continue to exist. Particle production causes the latter to expand like classical-matter-dominated universes at late times.
TL;DR: In this paper, quantum properties of the Yang-Mills homogeneous space model were considered in the Schrodinger representation, and the authors considered quantum mechanical properties of homogeneous spaces.
TL;DR: The title and discussion of this section of Sir Karl Popper’s book indeed strikes against his own philosophy of science-the idea that (responsible) controversy is indeed at the heart of any real scientific progress.
Abstract: In my view, the most curious section in this book is Chapter 3, Sec. 19: ’An Apology for Having Been Controversial’. The title and discussion of this section of Sir Karl Popper’s book indeed strikes against his own philosophy of science-the idea that (responsible) controversy is indeed at the heart of any real scientific progress (whether or not the leaders of the ongoing views [normal science] are happy or unhappy about this controversy!). Thus, I do not believe
TL;DR: In this paper, the motion of two-dimensional carriers in semiconductor heterojunctions, quantum wells and superlattices is discussed, with emphasis on subband dispersion parallel to the interfaces and on quantization in a perpendicular magnetic field.