Relativistic bound states in QCD

Mesons as bilocal fields in the harmonic approximation: A reassessment

“…Below we shall use propagator in momentum space, G z ( q ) , is conveniently parametrized through the functions E ( k , ) and p( k, ) (de-~( r ) = ( f ) v o r 2 , Vo=const . Pervushin and collaborators [2][3][4][5]131 have shown that with kernels of the form (61, this BSE is also manifestly 1 Lorentz covariant. E ( k ) = r n s i n p ( k ) + k cosp(k)-fp'(k)-=cos2p(k) , To solve the BSE, we should decompose $Lb) over the n Dirac y matrices [4,5,9,13].…”

“…From it they obtained the Schwinger-Dyson equation (SDE) determining the classical solution x,(x,y) or, equivalently, the dynamically generated quark selfmass operator 2 ( x , y ) and therefore also the "dressed" quark propagator G z . The fluctuations &(x, y ) around the classical solution xo(x,y) represent mesons [2][3][4][5]8,, so that the part of the action pertinent in this paper is the part containing &(x,y), denoted by we,: From we, one derives the Bethe-Salpeter equation (BSE) for the bilocal field &(x,y). This BSE Fourier transformed to momentum space is where T r a b , ( q l~) is the vertex function in momentum space of the quark-antiquark pair a,b and 29 =pa -pb, P = p a +pb.…”

“…Choosing an instantaneous interaction leads to a potential model. For the covariant generalization of the potential approach to the bound states, Pervushin and co-workers [4,5,13,14] found that the kernel should be of a special form [15], K-KT:…”

Monopole vacuum in non-Abelian theories

“…As was shown in the works [39,40,41], the instantaneous interaction of colour currents through a rising potential rearranges perturbation-theory series and leads to the constituent mass of the gluon field in Feynman diagrams; this changes the asymptotic-freedom formula at low momentum transferred, so that the coupling constant α QCD (q 2 ∼ 0) becomes finite. The rising potentials of the instantaneous interactions of colour currents [39,40,41] also lead to a spontaneous breakdown of the chiral invariance for quarks.…”

“…The rising potentials of the instantaneous interactions of colour currents [39,40,41] also lead to a spontaneous breakdown of the chiral invariance for quarks.…”