TY - JOUR

T1 - Thirring model in terms of currents

T2 - Solution and light-cone expansions

AU - Dell'Antonio, G. F.

AU - Frishman, Yitzhak

AU - Zwanziger, Daniel

N1 - Funding Information:
Work supported in part by the U. S. National Bureau of Standards.
Funding Information:
Work supported in part by funds from the National Science Foundation Grant No. GP-25610.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1972

Y1 - 1972

N2 - Exact expansions of operator products, in terms of c-number functions singular on the light cone and regular operators, are exhibited explicitly in the Thirring model. For the products ψ1(x)ψ1†(x′) and ψ2(x) ψ2†(x′) of fermion fields the expansion reduces to one term only, with the c-number function having a singularity on the light cone which depends on the coupling constant, and the regular operator depending only on the currents, which are free. The resulting formula allows one to calculate all Wightman functions in terms of current matrix elements and thereby provides a simple and complete solution to the Thirring model. The different charge sectors are realized as inequivalent irreducible representation spaces of the canonical current commutation relations, on which the charged field ψ acts as an intertwining operator.

AB - Exact expansions of operator products, in terms of c-number functions singular on the light cone and regular operators, are exhibited explicitly in the Thirring model. For the products ψ1(x)ψ1†(x′) and ψ2(x) ψ2†(x′) of fermion fields the expansion reduces to one term only, with the c-number function having a singularity on the light cone which depends on the coupling constant, and the regular operator depending only on the currents, which are free. The resulting formula allows one to calculate all Wightman functions in terms of current matrix elements and thereby provides a simple and complete solution to the Thirring model. The different charge sectors are realized as inequivalent irreducible representation spaces of the canonical current commutation relations, on which the charged field ψ acts as an intertwining operator.

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U2 - 10.1103/PhysRevD.6.988

DO - 10.1103/PhysRevD.6.988

M3 - Article

AN - SCOPUS:25544476303

VL - 6

SP - 988

EP - 1007

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 4

ER -