Geodesic
Thirring model. Asymptotic fields and $S$ matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 47-56 
A. K. Pogrebkov. Thirring model. Asymptotic fields and $S$ matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 47-56. http://geodesic.mathdoc.fr/item/TMF_1973_17_1_a4/
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     author = {A. K. Pogrebkov},
     title = {Thirring model. {Asymptotic} fields and $S$ matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {47--56},
     year = {1973},
     volume = {17},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_17_1_a4/}
}
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Asymptotic fields and the $S$ matrix are constructed in the Thirring model. It is shown that asymptotic fields exist only if the interacting field is a densely defined bilinear form. For this bilinear form Lorentz covariance is proved and also that the spectral condition holds for the generators of space-time translations. It is shown that locality holds formally only for a coupling constant equal to $\pm2\pi\surd{\overline{2n}}$, $n=0,1,2,\dots$

[1] W. Thirring, Ann. Phys., 3 (1958), 91 | DOI | MR | Zbl

[2] B. Klaiber, Lectures in Theoretical Physics, N. Y., 1968

[3] I. V. Volovich, V. N. Sushko, TMF, 9 (1971), 211

[4] G. F. Dell'Antonio, Y. Frishman, D. Zwanziger, Phys. Rev., D6 (1972), 988

[5] J. H. Lowenstein, Comm. Math. Phys., 16 (1970), 265 | DOI | MR

[6] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, 1958 | MR