Can QCD Be a Perturbation Theory of Hadrons?

Abstract

We have found that the S‐matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass‐shell in the bound states. The S‐matrix for bound states one should to construct by the projection of the Belinfante energy‐momentum tensor on the Gauss equation solution for the time component with the time‐axis chosen as the eigenvector of the bound state total momentum operator. We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.

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].…”

“…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]. Since in this work we are in-(1 1) terested only in the pseudoscalar mesons r , r 1 , K , K ' , we simply have Our solutions for p ( k ) , E T ( k ) , L l ( k ) , and L 2 ( k ) (obtained by the Adams-Bashfort method) agree with the ones in Ref.…”

“…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

“…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.…”