A continuum limit of the lattice gauge theory restricted to the hadron sector is proposed. Details of the appropriateness of formulating such a limit within a specific scheme of approximation are discussed for the quarkless hadron sector. The general method is then applied to the gauge fields, with the restriction that motions occur only along one spatial direction. This leads to a continuum eigenvalue equation for the spectrum of internal excitations associated with fluctuations in the length of the electric flux line. In addition, a nontrivial renormalization condition is encountered if one insists on a relativistic form for the spectrum. A speculative method for dealing with this condition is proposedthe method eliminates the lattice spacing and removes the coupling constant as a free parameter, as in dimensional transmutation. Alternative possibilities for restoring covariance in the hadronic sector of the theory are discussed.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)