Dynamical variables in the Bethe-Salpeter formalism

1955 ◽  
Vol 233 (1193) ◽  
pp. 248-266 ◽  
Keyword(s):  
Matrix Element ◽  
Bound States ◽  
Dynamical Variable ◽  
Wave Functions ◽  
Coupling Constant ◽  
Scattering States ◽  
The Matrix ◽  
The Masses

It is shown that a knowledge of the behaviour of the propagators around their singularities enables one to determine not only the masses of bound states, but also the matrix element of any dynamical variable between two bound states. One is thus enabled to find such a matrix element, to any order in the coupling constant, by the integration of certain expressions over the corresponding Bethe-Salpeter wave-functions. As a consequence, it is possible to find normalization and orthogonality properties of these wave-functions, which in turn lead to the condition which must be imposed on their singularities a t the origin. More light is thus shed on Goldstein’s difficulty concerning the existence of a continuous infinity of bound states. The formalism is extended to scattering states in which some of the particles may be composite—in particular, an expression for the S -matrix is obtained

Real and virtual processes in quantum electrodynamics

1952 ◽  
Vol 48 (4) ◽  
pp. 640-651 ◽  
Author(s):  
J. Hamilton
Keyword(s):  
Matrix Element ◽  
Power Series ◽  
Quantum Electrodynamics ◽  
Coupling Constant ◽  
Threshold Behaviour ◽  
Physical Processes ◽  
Matrix Formulation ◽  
The Matrix ◽  
Multiple Integrals ◽  
Analytic Behaviour

The S-matrix formulation of quantum electrodynamics, as developed by Feynman (3) and Dyson (1), expresses the matrix element for any process as a power series in the coupling constant, the coefficients of the series being, in general, rather complicated multiple integrals. These integrals contain singularities in their integrands, and in certain circumstances the coincidence of such singularities gives the S-matrix a non-analytic behaviour as a function of, for example, the total energy. The threshold behaviour of the S-matrix in the neighbourhood of energy values at which this phenomenon occurs has been investigated by Eden (2), who shows that the non-analytic behaviour is connected with the possible commencement of new physical processes, such as the creation of a particle.

scholarly journals DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS AND A BULK ABELIAN GAUGE FIELD

2010 ◽  
Vol 25 (35) ◽  
pp. 2933-2945 ◽  
Author(s):  
D. EBERT ◽  
V. CH. ZHUKOVSKY ◽  
A. V. TYUKOV
Keyword(s):  
Gauge Field ◽  
Effective Potential ◽  
Dynamical Variable ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Fifth Dimension ◽  
Fermion Masses ◽  
The Masses

The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A5 in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A5. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A5-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A5 field, the coupling constant and the radius are examined.

scholarly journals Bound states of dtμ, pdμ and t pμ mesomolecules

2019 ◽  
Vol 204 ◽  
pp. 05006 ◽  
Author(s):  
A. V. Eskin ◽  
V. I. Korobov ◽  
A. P. Martynenko ◽  
V. V. Sorokin
Keyword(s):  
Numerical Calculation ◽  
Bound States ◽  
Computer Code ◽  
Bound State ◽  
Wave Functions ◽  
Matrix Elements ◽  
Muonic Molecule ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of excited bound states of muonic molecules ptμ, pdμ, and dtμ is calculated on the basis of the stochastic variational method. The basis wave functions of the muonic molecule are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation, a computer code was written in the MATLAB system. As a result, the numerical values of bound state energies for excited P-states of muonic molecules ptμ, pdμ and dtμ were obtained.

scholarly journals Are wave functions uniquely determined by their position and momentum distributions?

1977 ◽  
Vol 20 (2) ◽  
pp. 182-201 ◽  
Author(s):  
J. V. Corbett ◽  
C. A. Hurst
Keyword(s):  
Fourier Transform ◽  
Large Class ◽  
Bound States ◽  
Integrable Function ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Scattering States ◽  
Momentum Distributions ◽  
Real Functions ◽  
Square Integrable Function

AbstractThe problem of determining a square integrable function from both its modulus and the modulus of its Fourier transform is studied. It is shown that for a large class of real functions the function is uniquely determined from this data. We also construct fundamental subsets of functions that are not uniquely determined. In quantum mechanical language, bound states are uniquely determined by their position and momentum distributions but, in general, scattering states are not.

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

Wave functions for weakly coupled bound states

1982 ◽  
Vol 25 (5) ◽  
pp. 2467-2472 ◽  
Author(s):  
S. H. Patil
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Weakly Coupled

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

scholarly journals RECENT RESULTS ON LIGHT HADRON SPECTROSCOPY AT BESIII

2011 ◽  
Vol 02 ◽  
pp. 183-187
Author(s):  
◽  
Y. CHEN
Keyword(s):  
Mass Spectrum ◽  
Matrix Element ◽  
Direct Measurement ◽  
International Workshop ◽  
Charm Physics ◽  
Hadron Spectroscopy ◽  
Threshold Enhancement ◽  
Light Hadron ◽  
The Matrix ◽  
Near Threshold

Several measurements on light hadron spectroscopy have been achieved with Beijing Spectrometry III (BESIII). BESII results such as a near threshold enhancement on the [Formula: see text] invariants mass spectrum namely X(1860) and a resonance X(1835) have been confirmed with 225 million J/ψ data accumulated from June 12, 2009 to July 28, 2009. Along with some other preliminary BESIII results including observations of X(1870), X(2120) and X(2370); the first direct measurement of a0(980)/f0(980) mixing; and an improved measurement on the matrix element of decay η′ → ππη have been reported at the 4th international workshop on charm physics.

scholarly journals A radical departure from the ‘steady-state’ concept in cosmology

1966 ◽  
Vol 290 (1421) ◽  
pp. 162-176 ◽  
Keyword(s):  
Steady State ◽  
Cosmic Rays ◽  
High Energy ◽  
Expansion Rate ◽  
Coupling Constant ◽  
De Sitter ◽  
Observable Universe ◽  
State Expansion ◽  
The Masses ◽  
Creation Of Matter

The results in this paper are based on an entirely different choice of the undetermined coupling constant f which appears in the theory of creation of matter. Previously f was chosen to make the steady-state expansion rate coincident with the observed expansion rate. Now that we take a much larger value for f , the corresponding steady-state expansion rate is much greater than the observed value. We interpret this difference as showing that we live in a wide, possibly temporary, fluctuation from the steady-state situation. The expansion rate in such a fluctuation follows the Einstein-de Sitter relations. The natural scale set by the new steady-state corresponds to the masses of clusters of galaxies, we obtain 10 13 M0 instead of 10 23 M@ for the ‘observable universe’. It is suggested that elliptical galaxies were formed early in the development of a fluctuation. Our discussion of high energy phenomena leads to im m ediate explanations of the energy spectrum of cosmic rays, of the presence of e + in cosmic rays and of the rate of energy production associated with radio sources.

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