Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

Atom Capture by Nanotube and Scaling Anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of a single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of such bound state. Binding of the polarizable atoms in the coupling constant interval η ²∈[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in the literature.     

Strings, world-sheet covariant quantization and Bohmian mechanics

The covariant canonical method of quantization based on the De Donder–Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard non-covariant canonical quantization, it is necessary to adopt a Bohmian deterministic hidden-variable equation of motion. In this way, string theory suggests a solution to the problem of measurement in quantum mechanics. PACS 11.25.-w; 04.60.Ds; 03.65.Ta     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

Non-negative Wigner functions in prime dimensions

According to a classical result due to Hudson, the Wigner function of a pure, continuous-variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [1]. For the case of systems of odd prime dimension, a different, greatly simplified method of proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods. PACS  03.65.Fd; 03.65.Sq; 03.67.-a     

On the harmonic gauge in the quantization of strings

We discuss the path integral quantization of the bosonic string in the (non-background covariant) harmonic gauge, confronting it with the recently proposed background covariant version. The critical dimension as well as the ghost number current anomaly is computed. Whereas the latter has been found to vanish in the background covariant harmonic gauge, we obtain the same result as in the conformal gauge. This apparent discrepancy is resolved by detecting a new anomaly pertaining to the background covariant version of the harmonic gauge.     

One-Dimensional Relativistic Dissipative System with Constant Force and its Quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltonian of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization on the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach. PACS: 03.30.+p, 03.65.−w, 45.05.+x, 45.20Jj     

A quantum mechanical description of the experiment on the observation of gravitationally bound states

Quantum states in the earth’s gravitational field have been observed, with ultra-cold neutrons falling under gravity. The experimental results can be described by the quantum mechanical scattering model presented here. We also discuss other geometries of the experimental setup, which correspond to the absence or the reversion of gravity. Since our quantum mechanical model quantitatively describes, particularly, the experimentally realized situation of reversed gravity, we can practically rule out alternative explanations of the quantum states, in terms of pure confinement effects. PACS  03.65.Ge; 03.65.Ta; 04.62.+v; 04.80.-y; 61.12.Ex     

High pressure behaviour of liquid caesium

This paper deals with the anomalous behaviour of liquid caesium at high pressures. A model for the phenomenon of electron collapse in the liquid phase, based on the anomalous density variation of liquid caesium with pressure has been proposed. The process of 6s→5d electron collapse is pictured as the formation of a virtual bound state and the tunnelling process accounts for the 6s⇌5d dynamic conversion. The same model together with the Friedel sum rule has been used to explain the resistivity variation of liquid caesium with pressure. The resistivity minimum observed in most of the liquid alkali metals in the low pressure region has been explained. The agreement with the experimental curve is good in the low pressure region whereas a large discrepancy exists at higher pressures. This may be due to the breakdown of the Ziman’s resistivity formula under conditions of resonance scattering.     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

Two-channel resonance scattering of waves and particles by point and planar defects

The shattering of a wave (quasiparticle) with a dispersion curve consisting of two quadratic branches by a planar defect is discussed. The analog of such a process is the scattering of a similar wave (quasiparticle) in a one-dimensional system by a point defect. It is shown that even when the defect is passive, i.e., has no internal degrees of freedom, scattering may become resonant. The physical explanation of this effect is that a wave with a lower-lying spectrum scattered by the defect is in resonance with a localized (bound) state emerging because of the interaction between the defect and a wave with a higher-lying spectrum. Zh. éksp. Teor. Fiz. 115, 306–317 (January 1999)     

Homotopy Classification of Bosonic String Field Theory

We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.     

Quantum Tunneling and Caustics under Inverse Square Potential

We examine the quantization of a harmonic oscillator with inverse square potential V(x)=(mω²/2) x²+g/x² on the line −∞<x<∞. We find that, for 0<g<3?²/(8m), the system admits a U(2) family of inequivalent quantizations allowing for quantum tunneling through the infinite potential barrier at x=0. These are a generalization of the conventional quantization applied to the Calogero model in which no quantum tunneling is allowed. The tunneling renders the classical caustics which arise under the potential anomalous at the quantum level, leading to the possibility of copying the profile of an arbitrary state from one side x>0, say, to the other x<0.     

Ambiguities on the Quantization of a One-Dimensional Dissipative System with Position Depending Dissipative Coefficient

For a one-dimensional dissipative system with position depending coefficient, two constant of motion are deduce. These constants of motion bring about two Hamiltonians to describe the dynamics of same classical system. However, their quantization describe the dynamics of two completely different quantum systems. PACS numbers: 03.20.+i; 03.30.+ p; 03.65.-w     

Unitarity bounds for gauged axionic interactions and the Green–Schwarz mechanism

We analyze the effective actions of anomalous models in which a four-dimensional version of the Green–Schwarz mechanism is invoked for the cancellation of the anomalies, and we compare it with those models in which gauge invariance is restored by the presence of a Wess–Zumino term. Some issues concerning an apparent violation of unitarity of the mechanism, which requires Dolgov–Zakharov poles, are carefully examined, using a class of amplitudes studied in the past by Bouchiat–Iliopoulos–Meyer (BIM), and elaborating on previous studies. In the Wess–Zumino case we determine explicitly the unitarity bound using a realistic model of intersecting branes (the Madrid model) by studying the corresponding BIM amplitudes. This is shown to depend significantly on the Stückelberg mass and on the coupling of the extra anomalous gauge bosons and allows one to identify standard-model-like regions (which are anomaly-free) from regions where the growth of certain amplitudes is dominated by the anomaly, separated by an inflection point, which could be studied at the LHC. The bound can even be around 5–10 TeV for a Z’ mass around 1 TeV and varies sensitively with the anomalous coupling. The results for the WZ case are quite general and apply to all the models in which an axion-like interaction is introduced as a generalization of the Peccei–Quinn mechanism, with a gauged axion.     

Dynamics of positron scattering from lithium,sodium and potassium atoms in hot and dense plasmas

The dynamics of positron scattering from the ground state of lithium, sodium and potassium atoms in hot and dense plasmas has been investigated by applying a two-state approximation that includes elastic scattering and rearrangement scattering. The wave functions and energies of the target alkali atoms have been determined quite accurately within the framework of the ’method of model potential’. An inclusive study was made on the effects of plasma screening on the differential and total cross sections for elastic scattering and positronium formation in the ground state for the incident positron energy lying within 10 eV to 500 eV. For the unscreened case, our present results agree reasonably with the results of other calculations. It was found that the cross sections suffer considerable change due to the effects of the background plasma.     

Inequivalent Representations of Commutator or Anticommutator Rings of Field Operators and Their Applications

Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations’ point of view has led to a recognition of a novel type of the superconducting phase transition. PACS: 03.70.+k, 05.30.−d, 11.10.−z, 74.20.Fg, 74.25.Bt, 74.78.Bz