scholarly journals New rational extensions of solvable potentials with finite bound state spectrum

2012 ◽  
Vol 376 (45) ◽  
pp. 2866-2872 ◽  
Author(s):  
Yves Grandati
Keyword(s):  
Bound State ◽  
Solvable Potentials ◽  
Bound State Spectrum

GROUND STATE CHARGE OF FERMION SOLITON SYSTEM IN 1+1 AND 3+1 DIMENSIONS

1993 ◽  
Vol 08 (04) ◽  
pp. 705-721
Author(s):  
M. RAVENDRANADHAN ◽  
M. SABIR
Keyword(s):  
Ground State ◽  
Energy State ◽  
Flow Analysis ◽  
Background Field ◽  
Bound State ◽  
Fermion Mass ◽  
Spectral Flow ◽  
Bound State Spectrum ◽  
Spectral Asymmetry ◽  
State Charge

Ground state charge of some fermion soliton system without C-invariance is calculated in 1+1 and 3+1 dimensions by a combination of adiabatic method and spectral flow analysis. Induced charge is calculated by evolving adiabatically the fields from a vacuum having a background field which has a zero energy state and spectral symmetry. The spectral flow is calculated by an analysis of the bound state spectrum. In 1+1 dimension our calculations are in agreement with the results already found in the literature. In 3+1 dimension we study the interaction of fermions with monopoles and dyons. In the case of monopoles, even though there is spectral asymmetry, ground state charge is found to be ±1/2. It is shown that ground state charge gets contribution only from the lowest angular momentum states and is discontinuous at the fermion mass.

CONSISTENT CANONICAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (21) ◽  
pp. 3823-3841 ◽  
Author(s):  
FUAD M. SARADZHEV
Keyword(s):  
Canonical Quantization ◽  
Bound State ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Schwinger Model ◽  
Canonical Variables ◽  
Bound State Spectrum

For the chiral Schwinger model, the canonical quantization formulation consistent with the Gauss law constraint is developed. This requires modification of the canonical variables of the model. The formulation presented is unitary and gauge-invariant under modified gauge transformations. The bound state spectrum of the model is established.

scholarly journals Comment on: “Some quantum aspects of a particle with electric quadrupole moment interacting with an electric field subject to confining potentials”

2020 ◽  
Vol 35 (25) ◽  
pp. 2075002
Author(s):  
Francisco M. Fernández
Keyword(s):  
Electric Field ◽  
Quadrupole Moment ◽  
Bound States ◽  
Electric Quadrupole ◽  
Bound State ◽  
Electric Quadrupole Moment ◽  
Bound State Spectrum ◽  
Moving Particle ◽  
Quantum Aspects

We analyze the results obtained from a model consisting of the interaction between the electric quadrupole moment of a moving particle and an electric field. We argue that the system does not support bound states because the motion along the [Formula: see text] axis is unbounded. It is shown that the author obtains a wrong bound-state spectrum for the motion in the [Formula: see text] plane and that the existence of allowed cyclotron frequencies is an artifact of the approach.

GROUND STATE CHARGE OF O(3) NONLINEAR σ MODEL SOLITONS IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (20) ◽  
pp. 3657-3667
Author(s):  
M. RAVENDRANADHAN ◽  
M. SABIR
Keyword(s):  
Angular Momentum ◽  
Ground State ◽  
Flow Analysis ◽  
Background Field ◽  
Bound State ◽  
Fermion Mass ◽  
Spectral Flow ◽  
Bound State Spectrum ◽  
Induced Charge ◽  
State Charge

The ground state charge of (2+1)-dimensional nonlinear σ model solitons is calculated by a combination of adiabatic method and spectral flow analysis. Induced charge is calculated by evolving adiabatically the fields from a vacuum having a background field which has spectral symmetry. The spectral flow is calculated by analyzing the bound state spectrum. It is shown that the ground state charge gets contribution only from the lowest angular momentum states and is discontinuous at the fermion mass. It is also shown that the ground state charge is independent of the way in which the final configuration is obtained.

Effect of Biquadratic Exchange Upon Ferromagnetic Two-Magnon Bound States. II. Anisotropic Exchange

1974 ◽  
Vol 52 (1) ◽  
pp. 33-39 ◽  
Author(s):  
D. A. Pink ◽  
R. Ballard
Keyword(s):  
Bound States ◽  
Exchange Interactions ◽  
Bound State ◽  
Exchange Term ◽  
Zero Temperature ◽  
Biquadratic Exchange ◽  
Anisotropic Exchange ◽  
Bound State Spectrum ◽  
Mode Pair ◽  
Isotropic Exchange

We have investigated the two-magnon bound state spectrum of a ferromagnetically ordered system for which the Hamiltonian contains an anisotropic bilinear exchange term, an anisotropic biquadratic exchange term, and a single-ion anisotropy term. The bound states, labelled by a wave vector q which we have taken to be in the [111] direction, were calculated by using zero-temperature Green functions. The principal results are: (i) the existence of single-ion bound states in the absence of single-ion anisotropy and conversely, their absence in the presence of such anisotropy, in contrast to the case in which the exchange interactions are isotropic; (ii) the appearance of an S mode for values of q, [Formula: see text]; (iii) the ordering of bound states for isotropic exchange interactions wherein the S0 mode lies below the S1-mode, D-mode pair and where the S1 mode lies below (above) the D mode if they lie below (above) the band, no longer holds.

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