Studying the Bethe–Salpeter formalism for interactions instantaneous in the rest frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be calculated almost entirely analytically with high accuracy, without the (numerical) diagonalization of the matrix representation obtained by expansion of the solut...

Abstract. To study the characteristic features of relativistic bound systems, the Bethe-Salpeter equation (BSE) for two equal mass spin 1/2 particles (like the deuteron) is solved in the cm-frame for a covariant separable interaction kernel. For that purpose the BSE is transformed to an eigenvalue problem which is diagonalized numerically. The Bethe–Salpeter amplitudes (BSAs) are obtained strai...

A one parameter, model confined-gluon propagator is employed in a phenomenological application of the Dyson-Schwinger and Bethe-Salpeter equations to the calculation of a range of πand ρ-meson observables. Good agreement is obtained with the data. The calculated quark propagator does not have a singularity on the real-p2 axis. A mass formula for the pion, involving only the vacuum, dressed quar...

In [1], it was conjectured that the permanent of a P-lifting θ of a matrix θ of degree M is less than or equal to the M th power of the permanent perm(θ), i.e., perm(θ) 6 perm(θ) and, consequently, that the degree-M Bethe permanent permM,B(θ) of a matrix θ is less than or equal to the permanent perm(θ) of θ, i.e., permM,B(θ) 6 perm(θ). In this paper, we prove these related conjectures and show ...

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P (x1, . . . , xN ; t|y1, . . . , yN ; 0) of finding N particles on lattice sites x1, . . . , xN at time t with initial occupation y1, . . . , yN at time t = 0.

It has recently been argued that there are no dynamic screening corrections to Salpeter’s enhancement factor in thermonuclear reactions, in the weak-screening limit. The arguments used were: 1) The Gibbs probability distribution is factorable into two parts, one of which, exp(−β∑ eiej/rij) (β = 1/kBT ), is independent of velocity space; and 2) The enhancement factor is w = 1 + βeZ1Z2〈φ〉 with 〈φ...

Relativistic Calculation of Structure Functions b 1,2 (x) of the Deuteron. Abstract The structure functions b D 1,2 (x) of the deuteron are studied within covariant approach. It is shown that usual nonrelativistic convolution model result in incorrect behavior of this structure functions at small x and violates the exact sum rules. Realistic calculations are carried out with the Bethe-Salpeter ...

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstat...

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However , we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies ...

We present a unitary relativistic quasi-potential model for describing the low-energy πN interaction, based on the equal time Bethe-Salpeter equation. It preserves the covariant structure of a relativistic spin 1/2 particle for the nucleon propagator, to be contrasted to other quasi-potential approximations.