Field-theoretical investigation of 2-d Coulomb systems with short-range Yukawa repulsion

In the present work a new regularization scheme based on a soft short-range Yukawa repulsion between the Coulomb gas particles is presented. This formulation is transcribed into a local sine-Gordon-like field theory involving two Bose fields, one the original massless sine-Gordon field corresponding to the long-range Coulomb interaction and an auxiliary massive field corresponding to the short-range Yukawa repulsion. The resulting Lagrangian is not Hermitian. Using the techniques of functional integration, an effective field theory the Coulomb field alone is obtained by integrating out the massive field. The resulting Lagrangian is now Hermitian. Then a generalization of Peierls' inequality is used to make a variational calculation of the ground state energy of the Coulomb system. A new method is used to derive the Kosterlitz-Thouless renormalization group equations, starting with the original sine-Gordon-like theory. The equations are identical to those found previously by other authors. A wave function renormalization is found to be necessary in addition to the normal ordering discussed by Coleman. A fermionized version of the theory is obtained, using the dictionary provided by Kogut and Susskind, which involves two Fermi fields and an electromagnetic potential. Position-space correlation functions are calculated at the critical point. The effective potential is computed in the one-loop approximation. A nonlinear field theory with derivative couplings is found to correspond to the two-dimensional Coulomb dipole gas in the functional integral formulation. A different type of a field theory is found for the dipole gas using the collective field formalism. A comparison is made with the critical behavior in the nonlinear Sigma model, the 2-D Heisenberg model, and the nonabelian gauge theories