Showing papers on "Quantization (physics) published in 1968"
TL;DR: In this paper, it was shown that for fields with integer-valued intrinsic angular momentum, the observed relation between spin and (exchange) statistics follows from continuity alone, parastatistics being excluded.
Abstract: Sufficiently nonlinear classical fields admit modes called kinks, whose number is strictly conserved in virtue of boundary conditions and continuity of the field as a function of space and time. In a quantum theory of such fields, with canonical commutation (not anticommutation) relations, kinks and their conservation still persist, and even if the intrinsic angular momentum is an integer, a rotating kink can have half‐odd angular momentum, if double‐valued state functionals are admitted. We formulate a natural concept of exchange appropriate for kinks. The principal result is that for fields with integer‐valued intrinsic angular momentum, the observed relation between spin and (exchange) statistics follows from continuity alone, parastatistics being excluded. It is likely that in the theories with even (odd) exchange statistics, suitable creation operators will commute (anticommute). We show that, while the rotational spectrum of a kink will in general possess both integer and half‐odd spin states, in fields with integer‐valued intrinsic angular momentum only one of these two possibilities will ever be observed for each kind of kink, and that there is a nonzero ``particle number'' (strictly conserved, additive, scalar quantum number) attached to half‐odd‐spin kinks of each kind. It then follows that a boson and a fermion kink will always differ in at least one particle number, as well as in spin, and that, in particular, every fermion kink will have some nonzero particle number. These results are consistent with the hypothesis that the spinor fields usually employed to describe half‐odd‐spin quanta are not fundamental, but are useful ``point‐limit'' approximations to operators creating or annihilating excitations in a nonlinear field of particular kinds of kinks in particular internal states.
303 citations
167 citations
TL;DR: In this article, the quantum theory of faster-than-light particles is studied following the earlier classical theory of Bilanuik, Deshpande, and Sudarshan and of Terletski.
Abstract: The quantum theory of faster-than-light particles is studied following the earlier classical theory of Bilanuik, Deshpande, and Sudarshan and of Terletski. The ingenious scheme of quantization formulated by Feinberg is seen, on closer examination, to violate Lorentz invariance. Another scheme of quantization involving a new physical postulate is formulated. The consistency and novel features of this formulation are discussed in some detail.
87 citations
TL;DR: The classical field produced by a prescribed external source was shown to be the generating functional of the tree-graph approximation to the corresponding quantum field theory in this paper, where the classical field was used as a source for the tree graph approximation.
Abstract: The classical field produced by a prescribed external source is shown to be the generating functional of the tree-graph approximation to the corresponding quantum field theory.
80 citations
TL;DR: In this article, the Schrodinger equation for the motion of an electric charge in the field of a magnetic monopole is examined to see how the quantization of the interaction constant follows from the requirement of rotational invariance.
74 citations
TL;DR: In this article, the authors apply quantum mechanics to the problem of a particle bound in an external gravitational potential, and find the following results which violate one's classical conception of the principle of weak equivalence: radii, frequencies, etc., depend on the mass of the bound particle; the binding energy has the wrong mass dependence; inertial forces do not look like gravitational forces; and there are mass-dependent interference effects.
64 citations
TL;DR: In this paper, a model of nuclear collective rotations is defined by giving the form of the velocity field versus position, and the usual quantization rules are then applied to form the quantal collective Hamiltonian.
TL;DR: The method of Froman and Froman for proving exact quantization conditions is reviewed in this paper, where the authors consider the behavior of the potential everywhere it is defined and prove the correctness of all known quantization rules for the one-dimensional and radial cases.
Abstract: The method of Froman and Froman for proving exact quantization conditions is reviewed This formalism, unlike the usual WKB approximation to which it bears a close resemblance, requires consideration of the behavior of the potential everywhere it is defined This approach leads to proofs that certain quantization conditions are exact without having to compare the results to solutions of the Schrodinger equation obtained by other means Using the formalism, we prove the correctness of all previously known exact quantization rules for the one‐dimensional and radial cases Furthermore, it is shown that exact quantization rules can be proved for two other potentials For one of these, no analytic solutions to the Schrodinger equation are known For the latter case, the proof is checked by numerical integration of the Schrodinger equation for a special case
TL;DR: In this article, a two-band model and Extremum of Band was proposed to measure the Fermi Momenta in Experiments with Ultrasound and by determining the cutoff of the cyclotron Resonance.
Abstract: CONTENTS Introduction 1 I. Space Lattice 2 II. Doubling of the Period 2 III. Electron Energy Spectrum 4 1. Expansion Near Extremum 4 2. Two-band Model 4 3. Deformation Theory 6 IV. Electron Spectrum in a Constant Magnetic Field 8 1. Classical Limit 8 2. Two-band Model and Extremum of Band 9 3. Quasiclassical Quantization 9 V. Specific Heat 10 VI. Magnetic Susceptibility 10 VII. Quantum Oscillations of the Susceptibility and of Other Thermodynamic and Kinetic Quantities 11 VIII. Electric Conductivity 14 1. Static Conductivity in a Constant Magnetic Field 14 2. Conductivity in the Absence of Constant Magnetic Field 14 3. Cyclotron Resonance 15 4. Magnetoplasma Waves 17 5. Optical Properties in the Infrared Region 19 IX. Measurement of the Fermi Momenta in Experiments with Ultrasound and by Determining the Cutoff of the Cyclotron Resonance 20 X. Tunnel Effect 20 XI. Phonon Spectrum 20 XII. Cited Literature 20
TL;DR: Capacitance observations of Landau levels in a two-dimensional electron gas induced in the inversion layer on a (100) surface of $p$-type silicon are reported in this paper.
Abstract: Capacitance observations of Landau levels in a two-dimensional electron gas induced in the inversion layer on a (100) surface of $p$-type silicon are reported. Evidence for surface quantization and the associated lifting of the spin and valley degeneracy are presented. An observed increase in the carrier threshold with increasing magnetic field is shown to be further evidence of surface quantization.
TL;DR: In this paper, a simple model effective Hamiltonians are used to examine the structure of magnetic sub-bands and the positions of the discrete Landau levels are accurately predicted by the first-order correction to the Onsager quantization rule given by Roth, even for strong magnetic fields.
Abstract: Simple model effective Hamiltonians are used to examine the structure of magnetic sub-bands. The positions of the discrete Landau levels are shown to be accurately predicted by the first-order correction to the Onsager quantization rule given by Roth, even for strong magnetic fields. The influence of the rational field condition, occuring when $\frac{l}{N}$ flux quanta pass through a unit cell, is investigated. The effect is pronounced when intraband or interband tunneling occurs. In this case the broadened sub-bands split into a cluster of $l$ smaller sub-bands. This fine structure may be roughly accounted for by use of an effective Hamiltonian based on the sub-band energy function $E(\mathbf{q})$.
Journal Article•
TL;DR: In this paper, it was shown that the exact solution of the Schrodinger equation can be expressed as a contour integral, where the energy operator consists of a time independent part Ho and a perturbation which depends linearly on time and is a projection operator onto a state I cp.
Abstract: It is shown that if the energy operator consists of a time-independent part Ho and a perturbation which depends linearly on time and is a projection operator onto a state I cp), the exact solution of the Schrodinger equation can be expressed as a contour integral. The Smatrix for such a problem possesses the triangular property and decomposes into elementary LandauZener factors, each of which mixes only a pair of states. Similar results are derived for the corresponding stationary problem. Some generalizations are considered, as well as examples, and the connection with previous solutions of the problem of electron detachment and of ionization in atomic and ionic collisions.
TL;DR: In this article, the conductivity of a semiconductor surface channel or a thin film is evaluated using a Green's-function formulation of perturbation theory, where boundary conditions at the surfaces of the channel are expressed in terms of a fluctuation potential rather than a Fuchs reflectivity parameter.
Abstract: The electrical conductivity in a semiconductor surface channel or a thin film is written in terms of integrals over a retarded current-current correlation function and evaluated using a Green's-function formulation of perturbation theory. The perturbation theory exhibits four new features. (1) The boundary conditions at the surfaces of the channel are expressed in terms of a fluctuation potential rather than a Fuchs reflectivity parameter. (2) The quantization of the eigenvalues for motion normal to the channel is explicitly incorporated into the theory. (3) The averaging procedure used to obtain the diagrammatic definition of the propagators and correlation functions is extended to include the effects both of screening and of graded interface impurity doping by permitting summation of multiple-scattering effects within planes of impurities parallel to the surface prior to the consideration of interference between these planes. (4) The propagators and conductivity are evaluated at arbitrary temperatures, using the Matsubara formalism. The conductivity is calculated explicitly in the quantum limit that the energy spacings $\ensuremath{\Delta}E$ between the eigenvalues for motion normal to the surface satisfy $\ensuremath{\Delta}E\ensuremath{\gg}\mathrm{kT}$ for the occupied eigenstates. The approximations needed to reproduce the Boltzmann-equation analysis by Stern and Howard of the extreme quantum limit are delineated. The effects of dispersion and quantized-state mixing are examined for a $\ensuremath{\delta}$-function model of the fluctuation potential. They are found to be significant if a quantized eigenvalue is near the Fermi energy or if the doping in the channel is highly nonuniform.
TL;DR: In this article, it was shown that the *-algebra of test-functions for a quantum field is reduced, i.e. for eachb∈ R,b≠ 0, there exists a positive continuous linear functionalW(a) onR withW(b)≠0.
Abstract: It is shown that the *-algebraR of test-functions for a quantum field is reduced, i.e. for eachb∈R,b≠0, there exists a positive continuous linear functionalW(a) onR withW(b)≠0.
TL;DR: In this paper, a study of the energy spectrum of a polaron in the presence of a magnetic field for the cases of weak and intermediate couplings, using Onsager's theory is made.
Abstract: A study is made of the energy spectrum of a polaron in the presence of a magnetic field for the cases of weak and intermediate couplings, using Onsager's theory. This theory makes use of the Bohr-Sommerfeld quantization rule, which has been derived with the WKB approximation and is therefore valid for large quantum numbers. Following an approach first formulated by Argyres, we prove that the energy spectrum of a polaron in a magnetic field obtained by using Onsager's theory is correct even for small quantum numbers like $n=0, 1, 2$, etc.
TL;DR: In this paper, a method for obtaining connections between residues at the poles and jumps through the cuts of the field matrix elements with the S -matrix on the mass shell was developed.
TL;DR: In this paper, a quantum-mechanical potential is introduced and the calculation of the binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case of nλ3≪1 (λ being the thermal wavelength).
Abstract: If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ3≪1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum.
TL;DR: In this article, the first quantum correction to a time correlation function was obtained by expanding the quantum-mechanical correlation function in powers of Planck's constant, which may be used to obtain quantum corrections to transport properties.
Abstract: The first quantum correction to a time correlation function is obtained by expanding the quantum‐mechanical correlation function in powers of Planck's constant. Quantum corrections to time correlation functions are of interest because they may be used to obtain quantum corrections to transport properties. An application of the formalism to nuclear spin‐lattice relaxation is included. A formal expression is obtained for the first quantum correction to the lattice time correlation functions. The effect of this correction on the relaxation time is indicated. The possibility of using the first quantum correction to calculate isotope effects on transport properties is discussed.
TL;DR: In this paper, the authors give new formulae permitting the calculation of time ordered but otherwise arbitrary correlation functions of electromagnetic field operators in terms of a class of quantum mechanical quasi-probability distribution functions.
Abstract: We give new formulae permitting the calculation of time ordered but otherwise arbitrary correlation functionsK of electromagnetic field operators in terms of a class of quantum mechanical quasi-probability distribution functions This class contains among others the socalledQ- andP-functions as well as the Wigner function
01 Jan 1968
TL;DR: In this paper, the problem of the reduction of the wave function in quantum theory is treated from a new standpoint, by combining Heisenberg's uncertainty relations with gravitation, quantitative limi tations on the sharpness of the structure of space-time are derived.
Abstract: The problem of the reduction of the wave function in quantum theory is treated from a new standpoint. First, by combining Heisenberg's uncertainty relations with gravitation, quantitative limi tations on the sharpness of the structure of space-time are derived. Second, the resulting uncertainty in space-time structure is incorporated into the equations for the propagation of the quantum-mechanical wave amplitudes. In the resulting theory an initially pure wave function generally develops in time into a mixture. A single pure wave function survives only as long as it corresponds to a sufficiently small spread in the position of any massive part of the system under investigation. Quantitative relations between the mass and the maximum coherent spread in the center-of-mass wave function of a single body are obtained.
TL;DR: In this article, the results of a previous paper on the gauge problem in quantum electrodynamics are generalized to the gravitational case and the difficulties connected with the quantization of the gravitational field are analyzed in the framework of axiomatic field theory.
Abstract: The results of a previous paper on the gauge problem in quantum electrodynamics are generalized to the gravitational case. In particular, the difficulties connected with the quantization of the gravitational field are analyzed in the framework of axiomatic field theory. For convenience, the simple case of weak gravitational field in vacuo is discussed. Even in this simple case, inconsistencies arise if one wants to combine the Einstein equations and quantum field theory. Under the assumptions: (1) existence of the vacuum, invariant under the Poincar\'e group, (2) existence of a representation of the Poincar\'e group such that the fields have tensor transformation properties, and (3) analyticity of the two-point function in the forward tube, it is proved that the Einstein equations for the gravitational potential have no solution apart from the trivial one ${R}_{\ensuremath{\mu}\ensuremath{
u}\ensuremath{\rho}\ensuremath{\sigma}}=0$. The result is obtained without assuming either local commutativity or the spectral condition or a positive metric in the Hilbert space. Thus the difficulties which arise in the quantization of the gravitational field have very little to do with the Hilbert-Lorentz condition, indefinite metric, etc.; rather, they are strongly connected with the definition of the Riemann tensor in terms of the gravitational potential. As a corollary of the above result, the representations of the Poincar\'e group for massless spin-2 particles in quantum field theory are shown to be essentially different from the corresponding ones of the classical case.
TL;DR: In this article, Souriau's space fiber quantifiant is shown under certain conditions to be realized in contact structure, and illustrative examples of contact structures are examined, and different geometric concepts in canonical quantization are discussed.
Abstract: Differential geometric concepts in canonical quantization are discussed. Souriau'sespace fibre quantifiant is shown under certain conditions to be realized in contact structure. Illustrative examples of contact structures are examined.
TL;DR: In this article, the authors considered the unified field theory of Heisenberg and co-workers in the framework of Bethe-Salpeter dynamics and proposed a non-canonical quantization procedure, which predicts the existence of spin-parity 0− mesons, a strongly bound family of solutions: a pion triplet, an eta singlet and a kaon doublet.
Abstract: The unified field theory of Heisenberg and co-workers is considered in the framework of Bethe-Salpeter dynamics. The approach suggests, in contrast to the Tamm-Dancoff formulations, the use of a Green’s function involving the baryon mass, in order to rectify deficiencies in the analytic properties of solutions hitherto found. On the basis of a noncanonical quantization procedure, the theory predicts the existence of two families of spin-parity 0− mesons,a) a strongly bound family of solutions: a pion triplet, an eta singlet and kaon doublets, supporting previous results of the unified field theory, andb) a new family of nearly degenerate mesons in the proximity of the baryon mass. The dynamical theory of the mutual baryon-baryon coupling constants to the pseudoscalar mesons is presented. The results are compared to experiment where available. It is pointed out that the dynamical solutions possess superconducting properties. In particular, the dynamical results for the pseudoscalar meson masses can be interpreted in analogy to the gap equations which arise in many-body fermion systems.