Showing papers on "Quantization (physics) published in 1984"
TL;DR: In this paper, a generalization of the dimensional reduction of supersymmetric string theories is introduced, which leads to spontaneous breaking of the supersymmetry, which has non-trivial consequences for the quantization and dynamics of the theory.
429 citations
TL;DR: In this article, a modified Hamiltonian equation of motion for density matrices was proposed to interpret upper bounds on the violation of quantum mechanics in different... phenomenological situations.
389 citations
TL;DR: In this article, a general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits, capable of generating squeezed-state or two-photon coherent-state signals.
Abstract: 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 applied to circuits capable of generating squeezed-state or two-photon coherent-state signals. Circuits capable of performing back-action-evading electrical measurements are also discussed.
375 citations
TL;DR: In this article, it was shown that in renormalizable models in four dimensions, the only infinity that can arise is at the one-loop order in the Yang-Mills coupling constant.
336 citations
TL;DR: In this paper, the topological action of multivalued wave functions can be derived in a model-independent way, in terms of the topology of the configuration space for indistinguishable particles in two dimensions.
Abstract: Because of complicated topology of the configuration space for indistinguishable particles in two dimensions, Feynman's path-integral formulation allows exotic statistics. All possible quantum statistics in two-space are characterized by an angle parameter $\ensuremath{\theta}$ which interpolates between bosons and fermions. The current formalisms in terms of topological action of multivalued wave functions can be derived in a model-independent way.
298 citations
Book•
01 Jan 1984
TL;DR: The components of Theoretical Spectroscopy are discussed in this paper, where the effects of strong fields on matter are discussed as well as the effect of field fluctuation on Spectrograms.
Abstract: The Components of Theoretical Spectroscopy. Physical Effects of Strong Fields on Matter. Foundation of Laser Theory. Topics in Laser Spectroscopy. Effects of Field Fluctuations on Spectroscopy. Elements of Electromagnetic Field Quantization. References. Index.
234 citations
TL;DR: In this article, it was shown that the quantized Hall current may always be expressed as the difference between diamagnetic currents flowing at the two edges, and that the high precision of the quantization may be aided by the establishment of a local equilibrium in each edge region.
Abstract: It is shown that the quantized Hall current may always be expressed as the difference between diamagnetic currents flowing at the two edges. It is argued that the high precision of the quantization may be aided by the establishment of a local equilibrium in each edge region. The basic ideas are illustrated by the discussion of a free two-dimensional electron gas in an infinite confining potential. Our derivation establishes the connection between quantum-mechanical and classical thermodynamic explanations for the quantum Hall effect.
204 citations
198 citations
TL;DR: In this paper, the authors discuss the quantization of Regge's discrete description of Einstein's theory of gravitation and show how the continuum theory emerges in the weak field long wavelength limit.
Abstract: We discuss the quantization of Regge's discrete description of Einstein's theory of gravitation We show how the continuum theory emerges in the weak field long wavelength limit We also discuss reparametrizations and conformal transformations
160 citations
TL;DR: In this paper, the fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered and it is shown to be a Kolmogorov K-system, and hence to have strong statistical properties.
157 citations
TL;DR: The Gaussian effective potential (GEP) is a natural extension of intuitive notions familiar from quantum mechanics as discussed by the authors, and it has been used as a guide to quantum field theories.
Abstract: We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
TL;DR: In this article, a principle of local definiteness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely, and it also allows us to formulate local stability.
Abstract: We discuss quantum fields on Riemannian space-time. A principle of local definiteness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows us 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.
Book•
01 Jan 1984
TL;DR: In this article, basic and well-established concepts of particle physics for the autodidact who is curious about recent developments in fundamental physics are elucidated for the uninitiated.
Abstract: This volume elucidates basic and well-established concepts of particle physics for the autodidact who is curious about recent developments in fundamental physics. Elementary quantum mechanics is a background must. Contents, abridged: The evolution of the particle concept before the advent of quantum mechanics. Nonrelativistic quantum mechanics and atomic physics. Relativistic quantum theory. Nuclear phenomena. Subnuclear phenomena. Index.
TL;DR: In this paper, it was shown that the effective lagrangian describing the critical fluctuations in a two-dimensional disordered electronic system in a transverse magnetic field contains a novel, topological term.
TL;DR: In this paper, a nonperturbative calculation of the effects of the electric field on electron-impurity scattering is presented, where a Boltzmann-type transport equation is derived with a nonlocal field-dependent collision integral.
Abstract: A formalism is developed which allows a nonperturbative calculation of the effects of the electric field on electron-impurity scattering. The single-site $T$ matrix is evaluated exactly and studied numerically for a model potential. For a dilute concentration of random impurities, the impurity-averaging procedure is carried out in a finite external field and a nonlinear integral equation is derived for the Green function. This equation is solved in an approximate, but consistent, manner. Finally, a quantum-transport equation is constructed with the generalized Baym-Kadanoff method of nonequilibrium quantum statistical mechanics. Special attention is paid to the field dependence of the collision integral. In particular, in the limit of slow spatial variations, a Boltzmann-type transport equation is derived with a nonlocal field-dependent collision integral.
TL;DR: In this paper, the authors pointed out some problems with the usual quantum-mechanical theory of electrodynamics in nonlinear dielectric media which is used in non-linear optics.
Abstract: We point out some problems with the usual quantum-mechanical theory of electrodynamics in nonlinear dielectric media which is used in nonlinear optics. In order to understand these problems, the Hamiltonian formulation of the theory is examined. It is found that many of the difficulties in the usual theory are a result of the fact that the canonical momentum for the interacting theory is not the same as that for the free electromagnetic field theory.
TL;DR: It was shown in this article that the ground state of a system showing the fractional quantum Hall effect must be degenerate; the non-degenerate ground state can only produce integral quantum Hall effects.
Abstract: It is shown that gauge-invariance arguments imply the possibility of the fractional quantum Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantum Hall effect must be degenerate; the nondegenerate ground state can only produce the integral quantum Hall effect.
TL;DR: In this paper, path integral Monte Carlo methods are used to study the effect of quantization of the orientational degrees of freedom of water (H2O), using the ST2 model.
TL;DR: In this paper, the eigenvalues of independent constants of motion form a locally regular lattice, in the limit σ √ √ n √ σ σ = 0.
Abstract: When Einstein-Brillouin-Keller quantization is possible, it applies to all conserved dynamical variables (not only to the Hamiltonian) and in particular to the time average of any dynamical variable. Thus, for an integrable system of $n$ degrees of freedom, the eigenvalues of $n$ independent constants of motion form a locally regular $n$-dimensional lattice, in the limit $h\ensuremath{\rightarrow}0$. Failure of doing that may be an indication of quantum chaos.
01 Jan 1984
TL;DR: In this paper, the authors describe a new formalism for analyzing a particular class of nonlinear optical devices, called two-photon devices, which operate as follows: several modes of the electromagnetic field are coupled via a nonlinearity in some material; two of the modes are the device's "signal" modes, the rest are "pump" modes; photons are created or destroyed in the signal modes two at a time.
Abstract: In this paper we describe a new formalism for analyzing a particular class of nonlinear optical devices. We call these devices two-photon devices because they operate as follows: several modes of the electromagnetic field are coupled via a nonlinearity in some material; two of the modes are the device’s “signal” modes, the rest are “pump” modes; photons are created or destroyed in the signal modes two at a time. Examples include parametric amplifiers and four-wave mixers. Two-photon devices are to be contrasted with one-photon devices, such as the laser, in which photons are created or destroyed in the signal mode one at a time. The formalism used in one-photon optics uses variables and quantum states suited to describing the output of a one-photon device.
TL;DR: In this article, the euclidean quantum theory corresponding to classical actions is constructed from below, preserving the classical limit, the large-N limit, and the perturbative expansion of the unstabilized theories.
TL;DR: In this article, a conformal symplectic (or conformal Poisson) structure is proposed, for which the bracket is the Poisson bracket modified by terms of order (1, 0) and (0, 1).
Abstract: After a review of the deformation (star product) approach to quantization, treated in an autonomous manner as a deformation (with parameter ħ) of the algebraic composition law of classical observables on phase-space, we show how a further deformation (with parameter β) of that algebra is suitable for statistical mechanics. In this case, the phase-space is endowed with what we call a conformal symplectic (or conformal Poisson) structure, for which the bracket is the Poisson bracket modified by terms of order (1, 0) and (0, 1). As an application, one sees that the KMS states (classical or quantum) are those that vanish on the modified (Poisson or Moyal-Vey) bracket of any two observables, multiplied by a conformal factor.
TL;DR: In this article, it is argued that a Born-Oppenheimer type approximation leads to dynamic potentials that make the nonobvious localization obvious, and applications are mentioned for photoselective chemistry, absorption spectroscopy, and chemical mechanisms.
Abstract: Coupled motion in many degrees of freedom is known to often show in classical mechanics unexpectedly localized quasiperiodic motion that could not have been anticipated from the potential function. Similar phenomena is observed in quantum theory and this article discusses the fundamental physics of such localization. It is argued below that a Born–Oppenheimer type approximation leads to dynamic potentials that make the nonobvious localization obvious. Applications are mentioned for photoselective chemistry, absorption spectroscopy, and chemical mechanisms.
TL;DR: In this article, the authors show how the state of one oscillator is reduced to a number eigenstate during the irreversible demolition counting process occurring in another coupled oscillator using standard demolition counting techniques (e.g., photoelectron counting).
Abstract: We show how quantum-counting quantum nondemolition measurements may be made using standard demolition counting techniques (e.g., photoelectron counting) for two oscillators coupled via a four-wave-mixing interaction. The analysis reveals how the state of one oscillator is reduced to a number eigenstate during the irreversible demolition counting process occurring in another coupled oscillator.
TL;DR: In this paper, the authors give special attention to the notion that the quantum frequency spectrum of a periodic system reduces to the classical spectrum in this limit and show that the classical result is not always recovered in the limit of large quantum numbers.
Abstract: The correspondence principle addresses the connection between classical and quantum physics. The simple statement that quantum mechanics reduces to classical mechanics in the limit where the principal quantum number n approaches infinity, while found in many textbooks, is not true in general. In this article we will give special attention to the notion that the quantum frequency spectrum of a periodic system reduces to the classical spectrum in this limit. Two simple counter‐examples—a particle in a cubical box, and a rigid rotator—will show us that the classical result is not always recovered in the limit of large quantum numbers. The usual textbook formulation of Bohr's frequency correspondence principle does not apply to all periodic systems, and the limits n→∞ and h→0 are not universally equivalent.
TL;DR: In this paper, it was shown that there exists a certain equivalence class of quantum field theories at finite temperature each of which produces the same statistical average, and the theories in this equivalent class are classified by multiplicities of field degrees of freedom and have a one to one correspondence with the choices of the path in the real-time path-ordered formulation of the statistical average.
Abstract: It is shown that there exists a certain equivalence class of quantum field theories at finite temperature each of which produces the same statistical averages The theories in this equivalent class are classified by multiplicities of field degrees of freedom and have a one to one correspondence with the choices of the path in the real‐time path‐ordered formulation of the statistical average Among them, thermo field dynamics is found to be the most convenient theory
TL;DR: A review of the current state of the theory of the quantum Hall effect is given in this article, where the integer values of the Hall conductance seen in systems with moderate disorder and predicted for systems with periodic modulation are fairly well understood.
TL;DR: In this paper, the de Broglie wave was used to reduce the number of degrees of freedom required for quantization of the quasiperiodic vibrational motion of a polyatomic system.
Abstract: Semiclassical quantization of the quasiperiodic vibrational motion of molecules is usually based on Einstein–Brillouin–Keller (EBK) conditions for the quantization of the classical actions. Explicit use of the EBK conditions for molecular systems of K degrees of freedom requires K quantization conditions. Therefore, explicit use of the EBK conditions becomes increasingly difficult if not impossible for polyatomic systems of three or more degrees of freedom. In this paper we propose a semiclassical quantization method which makes explicit use of phase coherence of the de Broglie wave associated with the trajectory rather than the EBK conditions. We show that taking advantage of phase coherence reduces the K quantization conditions to a single quantum condition—regardless of the number of degrees of freedom. For reasons that will become obvious we call this method ‘‘spectral quantization.’’ Polyatomic vibrational wave functions and energy eigenvalues are generated from quasiperiodic classical trajectories. The spectral method is applied to an ABA linear triatomic molecule with two degrees of freedom and to an anharmonic model of the molecule cyanoacetylene. The usefulness of the technique is demonstrated in this latter calculation since the cyanoacetylene model will have four coupled vibrational degrees of freedom.