Massless Pseudoscalar Fields and Solution of the Federbush Model

  • Published 2005


Generalizing methods, leading to solution in sufficiently simple models, one can hope to develop a solving technique for comparatively non-trivial and physically important problems. Examples of such, partly or entirely, solvable models are models of four-fermion interactions in two-dimensional space-time and related with them non-linear bosonic models of the sine-Gordon (SG) type. The relentless interest to these models is due to the fact that their non-Abelian four-dimensional analogs are successfully used for analysis and explanation of various non-perturbative effects in modern theory of strong interactions, such as: description of the processes of quark hadronization and phenomenon of spontaneous symmetry breaking [30], [37], [9]. They serve also as a “testing ground” for various non-perturbative methods [6]. Recently Faber, Ivanov in their series of papers [10]–[16], following Morchio et al. [28], [29], re-examined some ambiguities of the Thirring model [38], [22], [5] and elucidated existence of two-dimensional massless (pseudo-) scalar fields and their important properties for the model solution. The aim of the present work is to establish a similar role of those fields also for a direct step-by-step integration of the Heisenberg equations of the Federbush [17] model, and to advocate as a general method the corresponding linearization procedure, established previously for some non-relativistic and relativistic phenomenological models [24], [40]. In order to linearize Heisenberg equations we use the notion of physical fields [39]. We recall that Heisenberg equations are formal relations between operators, as long as they are not defined on a corresponding vector space [4]. This implies, that in order to give a physical meaning to the quantum-field-system description by means of the Heisenberg fields Ψ, it is necessary to represent them in a space of physical states, that, in turn,

Cite this paper

@inproceedings{KORENBLIT2005MasslessPF, title={Massless Pseudoscalar Fields and Solution of the Federbush Model}, author={S E KORENBLIT and V V SEMENOV Irkutsk}, year={2005} }