Supplement to Holonomic Quantum Fields, IV

This note is a supplementary paragraph to our preceding paper IV [1], Our aim here is to relate the field operators in [1], constructed directly from the commutation relations, to the known models of Lagrangian field theory in two space-time dimensions; namely the Federbush model ([2]) and the massless Thirring model ([3]). In fact this connection has been known in the literature ([4] [5]), which we have come to know only lately. We wish to thank Professor N. Nakanishi for drawing our attention to the articles [5] [6]. As such, the content of this note is not essentially new, except for the exact computation of the n-point functions for the Federbush model (see § 3). The plan of this note is as follows. In Section 1 we prepare several formulas needed in subsequent paragraphs. In Section 2 we give the operator solutions of the Federbush model ([4] [5] [6]) in terms of the operators introduced in Section 1. By identifying the current with the free one we check the validity of the microcausality and the equations of motion. In Section 3 we calculate their asymptotic fields, iS-matrix ([5]) and the n-point functions by appealing to the results of IV [1]. In Section 4 we follow the analogue of Section 2 for the Thirring model, by using the operators introduced in II [7].