相对论类空方程

根据Dirac类空自洽性条件的思想,通过引入类空因子定义了类空波函数.它的物理部分与Bethe-Salpeter波函数相一致.利用普适的相互作用核的重排技术,导出了对于束缚态和散射态的相对论类空方程,并且将它们推广到多粒子的情形.也得到了束缚态类空波函数的归一化条件和散射态类空方程的非齐次项的解.因此,建立起了相对论类空方程体系.     

Space-Like Form of Bethe-Salpeter Equation: Scatter State

According to Dirac, and based on our space-like form of Bethe-Salpeter equation of bound state, we extend the definition of the space-like wavefunctions and derive out the spacelike form of Bethe-Salpeter equation for scatter state. The solution of the inhomogeneous term is also obtained in detail so as to clarify the significance of inhomogeneous space-like form of Bethe-Salpeter equation for scatter state. Moreover the translation method is finally discussed.     

Space-Like Form of Bethe-Salpeter Equation: Bound State

According to Dirac's principle, we apply the space-like consistency conditions in a relativistic theory to two-particle system and then define the space-Like wavefunctions through introducing a space-like factor, which is equivalent to Bethe-Salpeter wavefunction in physical content. The space-like form of Bethe-Salpeter equation of bound states is derived in terms of the universal rearranging technology of interaction kernel. Its advantages are of explicit Lorentz-covariant form and the difficulty of ghost states is automatically overcome. We also discuss the normalization condition of the space-like function.     

Calculation of the Electromagnetic Form Factor of the Kaon

The wavefunctions of the bound state of the charged kaon are obtained from the Bethe-Salpeter equation with the phenomenological vector-vector-type Aat-bottom potential. The physical space-like electromagnetic form factor of the charged kaon is calculated. The results calculated give a good fit to the experimental values.     

Generalized vector dominance and the pion form factor

We have calculated the pion form factor using the bound state Bethe-Salpeter amplitudes and the quark form factor of a relativistic quark model. We obtain a generalized vector dominance structure and an asymptotic behaviour in the space-like region F_π(Q)² −0.33 GeV²/Q².     

THE ELECTROMAGNETIC FORM FACTOR OF THE O- MESON IN THE STRATON MODEL

In the straton model,the wave functions of the 0^- meson can be obtained numerical-ly from the Wick rotated Bethe-Salpeter equation.The problem of comparing experi-ment with the mesonic electromagnetic form factor calculated by analytical continua-tion of the wave functions from the Euclidean space back to the Minkowski space isan unsolved problem.On the basis of analyzing the analytic property of the formfactor,we proved that by choosing a special reference system in which the photon isspace-like,one may calculate the physical space-like electromagnetic form factor dire-ctly from the Euclidean B-S wave functions of the meson in the Euclidean space.As an example,we calculated the electromagnetic form factor of the pseudoscalarmeson by using the wave functions corresponding various choices of parameters.Pre-liminary results show that the theoretical calculation may be in accordance with experi-ment by appropriately choosing the parameters.     

Correction to Goldstein Equation from the Gluon Condensate Diagram

An exact Goldstein solution of the Bethe-Salpeter equation including the gluon condensate in the background field QCD is discussed.We find that the gluon condensate diagram makes quark and anti-quark more close to form a bound state.     

Covariant description of Hamiltonian form for field dynamics

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface.     

Bound-state,Bethe—Salpeter solutions with conjugate pairs of complex coupling constants

Solutions are obtained to the Bethe-Salpeter equation describing bound states of two massive scalars interacting via the exchange of a third, massive scalar. Covariance of the equation implies that the interaction is retarded, and in part because the energy appears more than once in the equation, a Hamiltonian for the bound state does not exist. Thus in contrast to the Schrodinger equation, the Bethe-Salpeter equation is solved by specifying the energy and solving for the coupling constant as an eigenvalue. Although the Bethe-Salpeter equation is derived from a Lagrangian with real coupling constants, depending on the value of the energy and the masses of the scalars, some values of the coupling constant that satisfy the Bethe-Salpeter equation are complex and always occur in conjugate pairs. The unexpected existence of solutions with real energy and a complex coupling constant raises the possibility that there are also resonance solutions with real values of the coupling constant and complex energy. Supported by a grant from the Ohio Supercomputer Center. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

On quantum electrodynamics of two-particle bound states containing spinless particles

We develop here the general treatment arising from the Bethe-Salpeter equation for a two-particle bound system in which at least one of the particles is spinless. It is shown that a natural two-component formalism can be formulated for describing the propagators of scalar particles. This leads to a formulation of the Bethe-Salpeter equation in a form very reminiscent of the fermion-fermion case. It is also shown, that using this two-component formulation for spinless particles, the perturbation theory can be systematically developed in a manner similar to that of fermions. Quantum electrodynamics for scalar particles is then developed in the two component formalism, and the problem of bound states, in which one of the constituent particles is spinless, is examined by means of the means of the Bethe-Salpeter equation. For this case, the Bethe-Salpeter equation is cast into a form which is convenient to perform a Foldy-Woutyhuysen transformation which we carry out, keeping the lowest-order relativistic corrections to the nonrelativistic equation. The results are compared with the corresponding fermion-fermion case. It is shown, as might have been expected, that the only spin-independent terms that occur for the fermion-fermion system which do not occur for bound scalar particle cases, is the zitterbewegung contribution. The relevance of the above considerations for systems that are essentially bound by electromagnetic interactions, such as kaonic hydrogen, is discussed.     

Partial diagonalization of Bethe-Salpeter type equations

We consider an equation of the Bethe-Salpeter type, with arbitrary potential and kernel, respectively, for space-like momentum transfer. The invariance group of the equation is then the Lorentz-group in three dimensions, the O(1, 2) group. The standard procedure for the diagonalization of such equations (valid for square integrable solutions only) is generalized to include the case of power bounded solutions, by means of a generalized O(1, 2) expansion formalism. The result is a two-dimensional integral equation for the O(1, 2) expansion coefficients. The right-most l-plane singularities of these determine the asymptotic behaviour of the amplitudes as in ordinary Regge theory. The formalism can be applied to other dynamical equations possessing O(1, 2) symmetry.     

Electromagnetic properties of baryons in a relativistic quark model

Results on electromagnetic form factors of the nucleon and photon transition form factors of non-strange baryon resonances calculated in a relativistically covariant quark model based on the Bethe-Salpeter equation are presented. The relevance of the instanton-induced quark interaction on these properties is discussed.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.10.St Bound and unstable states; Bethe-Salpeter equations - 12.39.Ki Relativistic quark model - 12.40.Yx Hadron mass models and calculations - 13.40.Gp Electromagnetic form factors     

Calculations of some properties of the kaon

The wave functions of the bound state of the charged kaon are obtained from Bethe-Salpeter equation with the phenomenological vector-vector-type flat-bottom potential. The physical spacelike electromagnetic form factor of the charged kaon is calculated from the wave functions. The radius of the kaon is given from the electromagnetic form factor. The decay constant f _K of the kaon is estimated by the relationship between the decay constant and the normalization factor derived from the axial-vector Ward identity. All calculated results give a good fit to the experimental values.     

Electromagnetic Form Factor of Charged Scalar Meson

Wavefunctions and the electromagnetic form factor of charged scalar mesons are studied with the vector-vectortype fiat-bottom potential model under the framework of the spinor-spinor Bethe-Salpeter equation. The obtained results are in agreement with other theories.     

A variational principle for bound states in quantum field theory

We develop a Rayleigh-Ritz variational method for estimating relativistic, multi-particle bound state energies in any (weak-coupling) quantum field theory. A comparison is made with bound state energies derived from the Bethe-Salpeter equation in the Wick-Cutkosky model. Possible applications to QCD are discussed.     

O(4) Expansion of the Ladder Bethe-Salpeter Equation

The Bethe-Salpeter amplitude is expanded on a hyperspherical basis thereby reducing the original four-dimensional integral equation into an infinite set of coupled one-dimensional ones. It is shown that this representation offers a highly accurate method to determine numerically the bound state solutions. For generic cases only a few hyperspherical waves are needed to achieve convergence, both for the ground state as well as for radially or orbitally excited states. The wave function is reconstructed for several cases and in particular it is shown that it becomes independent of the relative time in the nonrelativistic regime. Received July 18, 1996; accepted in final form October 2, 1996     

Two-fermion bound states within the Bethe-Salpeter approach

To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the nonrelativistic ones and to the results given by light-front dynamics.     

The Barbieri-Remiddi Solution of the Bound-State Problem in QED

We derive the so-called Barbieri-Remiddi solution of the Bethe-Salpeter equation in QED in its general form and discuss its application to the bound-state energy spectrum.     

Darboux Transformations Between Δα=sinh α and Δα=sin α and the Application to Pseudo-Spherical Congruences in R2,1

In this Letter, it is proved that by using Darboux transformation, from a known solution of the sinh-Laplace equation (resp. sine-Laplace equation), new solutions of sine-Laplace equation (resp. sinh-Laplace equation) are obtained explicitly. The corresponding geometrical configuration is the space-like pseudo-spherical line congruence with two focal surfaces of negative constant curvature being space-like and time-like, respectively.     

一种新的可能的复合场的量子场论

本文引进了双粒子的双重定域场算符和Bethe-Salpeter的算子方程来描述复合场的运动和变化,进一步扩展了H-N-Z的束缚态场论。