scholarly journals BOUND STATES FROM REGGE TRAJECTORIES IN A SCALAR MODEL

2001 ◽  
Vol 16 (27) ◽  
pp. 4377-4400
Author(s):  
A. WEBER ◽  
J. C. LÓPEZ VIEYRA ◽  
C. R. STEPHENS ◽  
S. DILCHER ◽  
P. O. HESS
Keyword(s):  
Renormalization Group ◽  
Bound States ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Ladder Approximation ◽  
Scalar Model ◽  
Scalar Theory ◽  
Regge Trajectories ◽  
Bound State Spectrum ◽  
Compare And Contrast

The calculation of bound state properties using renormalization group techniques to compute the corresponding Regge trajectories is presented. In particular, we investigate the bound states in different charge sectors of a scalar theory with interaction ϕ†ϕχ. The resulting bound state spectrum is surprisingly rich. Where possible we compare and contrast with known results of the Bethe–Salpeter equation in the ladder approximation and, in the nonrelativistic limit, with the corresponding Schrödinger equation.

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.

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.

scholarly journals The SUSY Yang–Mills plasma in a T-matrix approach

2015 ◽  
Vol 30 (24) ◽  
pp. 1550145 ◽  
Author(s):  
Gwendolyn Lacroix ◽  
Claude Semay ◽  
Fabien Buisseret
Keyword(s):  
Gauge Group ◽  
Bound States ◽  
Bound State ◽  
Lattice Data ◽  
Superstring Theory ◽  
Matrix Formulation ◽  
Yang Mills ◽  
Bound State Spectrum ◽  
T Matrix ◽  
Arbitrary Gauge

In this paper, the thermodynamic properties of [Formula: see text] supersymmetric Yang–Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from noncritical closed superstring theory leads to a prediction for the value of the deconfining temperature [Formula: see text] that agrees with recent lattice data. The deconfined phase is studied by resorting to a [Formula: see text]-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1–5) [Formula: see text], where the interactions are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 [Formula: see text] for any gauge group. The equation of state is then computed numerically for [Formula: see text] and [Formula: see text], and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of nonsupersymmetric Yang–Mills when normalized to the Stefan–Boltzmann pressure and expressed as a function of [Formula: see text].

Variational solution of bound states in a charged interacting scalar-field theory

1988 ◽  
Vol 66 (11) ◽  
pp. 969-971 ◽  
Author(s):  
J. W. Darewych ◽  
A. D. Polozov
Keyword(s):  
Weak Coupling ◽  
Bound States ◽  
Scalar Fields ◽  
Delta Function ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Weak Coupling Limit ◽  
Variational Approximation ◽  
Coupling Constant ◽  
Spatial Dimensions

Two interacting [Formula: see text] scalar fields in N spatial dimensions are investigated using the Gaussian variational approximation. The interaction is taken to be in the form [Formula: see text]. Two-particle bound-state solutions are obtained in the domain g < 2λ for N = 1 and 2. The nonrelativistic limit, which is also the weak-coupling limit, is shown to correspond to an attractive delta-function interaction. For N = 3, the Gaussian ansatz suggests triviality of the theory, in that the renormalized coupling constant is identically zero.

scholarly journals STRONG COULOMB COUPLING IN THE TODOROV EQUATION

1996 ◽  
Vol 11 (30) ◽  
pp. 5303-5325 ◽  
Author(s):  
M. BAWIN ◽  
J. CUGNON ◽  
H. SAZDJIAN
Keyword(s):  
Bound States ◽  
Narrow Band ◽  
Relativistic Quantum ◽  
Goldstone Boson ◽  
Bound State ◽  
Coupling Constant ◽  
Coulomb Coupling ◽  
Strong Coulomb ◽  
Bound State Spectrum ◽  
Adjoint Extension

A positronium-like system with strong Coulomb coupling, considered in its pseudoscalar sector, is studied in the framework of relativistic quantum constraint dynamics with the Todorov choice for the potential. Case’s method of self-adjoint extension of singular potentials, which avoids explicit introduction of regularization cut-offs, is adopted. It is found that, as the coupling constant α increases, the bound state spectrum undergoes an abrupt change at the critical value α=αc=1/2. For α>αc, the mass spectrum displays, in addition to the existing states for α<αc, a new set of an infinite number of bound states concentrated in a narrow band starting at mass W=0; all the states have indefinitely oscillating wave functions near the origin. In the limit α→αc from above, the oscillations disappear and the narrow band of low-lying states shrinks to a single massless state with a mass gap with the rest of the spectrum. This state has the required properties to represent a Goldstone boson and to signal spontaneous breakdown of chiral symmetry.

Effect of Biquadratic Exchange upon Ferromagnetic Two-Magnon Bound States

1972 ◽  
Vol 50 (15) ◽  
pp. 1728-1735 ◽  
Author(s):  
D. A. Pink ◽  
P. Tremblay
Keyword(s):  
Wave Vector ◽  
Bound States ◽  
Bound State ◽  
Heisenberg Ferromagnet ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Biquadratic Exchange ◽  
Bound State Spectrum ◽  
Magnon Spectrum ◽  
The One

We have calculated the effects of an isotropic biquadratic exchange term having a coupling constant of moderate size [Formula: see text] upon the two-magnon bound state spectrum of an otherwise Heisenberg ferromagnet, with or without single-ion anisotropy, at zero temperature. The bound states are labelled by a wave vector q which we have taken to be in the [111] direction. The two principal results found are: (i) The large effect that K/J has in localizing the '"exchange coupled" bound state, S1 for all values of q above the two-magnon band, when it is sufficiently negative and the spin or pseudo-spin magnitude is of sufficient size. (ii) The change in the value of the wave vector, as K/J changes, at which the one-magnon spectrum crosses that of the "single-ion" bound state, S0.

Laplace Transformation Approach to the Spin Symmetry of the Mie-Type Potential with a Coulomb Tensor Interaction

2014 ◽  
Vol 69 (3-4) ◽  
pp. 111-121 ◽  
Author(s):  
Mahdi Eshghi ◽  
Sameer M. Ikhdair
Keyword(s):  
Bound States ◽  
Spin Symmetry ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Tensor Interaction ◽  
Special Cases ◽  
The Laplace Transform ◽  
Potential Parameters ◽  
Schrödinger System ◽  
Type Potential

The Dirac equation is solved exactly under the condition of spin symmetry for a spin 1=2 particle in the field of Mie-type potential and a Coulomb-like tensor interaction via the Laplace transform approach (LTA). The Dirac bound state energy equation and the corresponding normalized wave functions are obtained in closed forms with any spin-orbit coupling term k. The effects of the tensor interaction and the potential parameters on the bound states are also studied. It is noticed that the tensor interaction removes degeneracy between two states in spin doublets. Some numerical results are given and a few special cases of interest are presented. We have demonstrated that in the nonrelativistic limit, the solutions of the Dirac system converges to that of the Schrödinger system. The nonrelativistic limits of the present solutions are compared with the ones obtained by findings of other methods. Our results are sufficiently accurate for practical purpose.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

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.

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