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in quantum chromodynamics ( qcd ) , the physics of strongly interacting particles is described in terms of quarks and gluons as the dynamical degrees of freedom ( dof ) . in the low - energy regime , qcd can be approximated by an effective field theory ( eft ) using hadronic dynamical dof . to that end ,
one writes down the most general lagrangian consistent with the assumed symmetries of the fundamental theory  @xcite .
in addition , one needs a power - counting scheme for the expansion of physical observables .
the interaction of the pseudoscalar octet @xmath0 with the baryon octet is largely constrained by spontaneous symmetry breaking @xcite .
it is also interesting to investigate the coupling of the vector - meson octet to the baryon octet .
the situation is more complex , because a lorentz - invariant description of spin-1 systems introduces unphysical degrees of freedom .
therefore , one imposes constraints which , for an interacting theory , may lead to relations among the coupling constants of the lagrangian .
we investigate the lowest - order effective lagrangian for the interaction of the vector - meson octet with the baryon octet by performing a classical dirac constraint analysis  @xcite . for the quantized theory we demand that it is perturbatively renormalizable in the sense of effective field theory @xcite . for the pure vector - meson sector ,
such an investigation results in a massive su(3 ) yang - mills theory  @xcite . for the interaction of the vector mesons with the baryons
we search for additional relations among the coupling constants .
the most general effective lagrangian for a system of a massive vector - meson octet interacting with a massive baryon octet can be written as @xmath1 where the su(3 ) indices @xmath2 range from @xmath3 to @xmath4 .
the three coupling constants @xmath5 , @xmath6 , and @xmath7 are dimensionless . in eq .
( [ lagrangian ] ) , the ellipses stand for `` nonrenormalizable '' higher - order interactions , which we assume to be suppressed by powers of some large scale , as well as for interactions with other hadrons .
we take the lagrangian to be invariant under _ global _
su(3 ) transformations . for the vector - meson self interaction , the constraint analysis of refs .
@xcite has already been incorporated , leading to a reduction from five independent couplings to one single coupling @xmath5 .    in the canonical formalism ,
the momentum field variables conjugate to the field variables are given by @xmath8 because @xmath9 and @xmath10 are anti - commuting variables , we consider the convention of taking fermionic derivatives from the left for the adjoint field and from the right for the field .
using these relations , we immediately see that the velocities can not be expressed in terms of the momenta . in this case
, we can not go from the configuration space of the system to its phase space . to define the hamiltonian of the system
, we introduce three so - called primary constraints @xcite , @xmath11 here , a relation such as @xmath12 denotes a weak equation in dirac s sense @xcite , namely that one must not use one of these constraints before working out a poisson bracket . in total , eq .
( [ p ] ) amounts to 8 constraints for the vector mesons and @xmath13 constraints for the baryons .
we introduce unknown lagrange multiplier functions @xmath14 , define a constraint hamiltonian ( density ) @xmath15 , and construct the total hamiltonian ( density ) in terms of a legendre transformation , @xmath16    l*6cr case & total dof & constraints & physical dof + free vector fields & 64 & 16 & 48 + free dirac fields & 128 & 64 & 64 + interacting theory & 192 & 80 & 112 +    the requirement that eqs .
( [ p ] ) have to be zero throughout all time results in @xmath17 where @xmath18 .
equation ( [ poisson1 ] ) is a so - called secondary constraint , and , therefore , we obtain 8 additional constraints .
evaluating the poisson bracket of @xmath19 and @xmath20 results in an equation for the lagrange multiplier @xmath21 . from eqs .
( [ poisson2 ] ) and ( [ poisson3 ] ) we can solve for the lagrange multipliers @xmath22 and @xmath23 , respectively . at this stage , we have solved for all the lagrange multipliers and have generated the correct number of constraints . as a result of dirac s constraint analysis , at the classical level
we have a self - consistent theory with the correct number of constraints and thus the correct number of physical dof without any relation among the couplings .
pertubative renormalizability in the sense of eft requires that the ultraviolet divergences of loop diagrams can be absorbed in the redefinition of the masses , coupling constants , and fields of the _ most general _ effective lagrangian . as in refs .
@xcite , we expect additional relations among the coupling constants due to the perturbative renormalizability condition . redefining the fields and parameters
, the counter - term lagrangian reads @xmath24 by comparing the expression for @xmath25 obtained from the @xmath26- and @xmath27-vertex functions , we can test whether there are relations among the coupling constants @xmath5 , @xmath6 , and @xmath7 .
the `` worst case '' would be if all couplings were independent .
a different scenario is a type of universality , relating @xmath5 to a linear combination of @xmath6 and @xmath7 .
finally , all couplings could be expressible in terms of a single parameter .
at the classical level , the standard lowest - order su(3)-invariant lagrangian involving three independent coupling constants @xmath5 , @xmath6 , and @xmath7 is a self - consistent starting point .
this was explicitly shown using dirac s method .
whether the requirement of perturbative renormalizability implies additional constraints among the couplings remains to be seen .
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we describe a constraint analysis for the interaction of the vector - meson octet with the baryon octet . applying dirac s hamiltonian method 
 , we verify that the standard interaction in terms of two independent su(3 ) structures is consistent at the classical level . 
 we argue how the requirement of self consistency with respect to perturbative renormalizability may lead to relations among the renormalized coupling constants of the system .