New meron-type solutions

Abstract

New meron-type solutions are constructed to the Thirring model. During the last few years a considerable amount of work has been devoted to the study of the classical solutions of field equations within various fields of theoretical physics. An interpretation of classical solutions was given in the form of vacuum expectation values of quantum fields. This has represented an interesting ground of investigation for a deeper understanding of the formal aspects of the theory (1 ). Among the classical solutions, instanton and meron solutions had a particular place. Since the first instanton solutions (2), the one and multiple instanton solutions were found (3) and the determinants, the one loop contribution in the presence of the background field of the classical solutions, were calculated (4). Self-coupled spinor models were also studied in this line of research, and meron- and instanton- type solutions of pure Thirring (5) and G~rsey (6) models were found (7). In this paper, we construct new meron-type solutions for the original Thirring model. We start with tile Lagrangian in the Euclidean domain