Exact Solution of the Multiflavor Gross-Neveu Model

摘要

The Polyakov-Wiegmann fermionization of the SU(2) principal chiral field in two dimensions, i.e., the 0(4) sigma model, is fulfilled in a rigorous fashion to the end. Instead of solving a higher-spin fermionic theory, we study the multiflavor chiral-invariant Gross-Neveu model, strictly shown to be equivalent to the initial bosonic theory if the number of flavors tends to infinity. The Bethe-ansatz diagonalization of the relativistic model is performed, the filling of the Dirac sea is accomplished, the physical vacuum and excitations with finite energy and momentum are constructed. A correlation between the two couplings in the model is found necessary. The S-matrix for the massive physical excitations to be the same as in the one-flavor case. This does not corroborate the assumption that the fundamental particles of the sigma model are in the vector representation of O(4). The renormalization-group beta function agrees with a one-charged solution in perturbations theory. 24 refs. (Atomindex citation 18:091407)