Geodesic
Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 2, pp. 211-231 
I. V. Volovich; V. N. Sushko. Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 2, pp. 211-231. http://geodesic.mathdoc.fr/item/TMF_1971_9_2_a3/
@article{TMF_1971_9_2_a3,
     author = {I. V. Volovich and V. N. Sushko},
     title = {Constructive field theory: {Thirring} model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. {I.~Local} field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {211--231},
     year = {1971},
     volume = {9},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_2_a3/}
}
TY  - JOUR
AU  - I. V. Volovich
AU  - V. N. Sushko
TI  - Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 211
EP  - 231
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_9_2_a3/
LA  - ru
ID  - TMF_1971_9_2_a3
ER  - 
%0 Journal Article
%A I. V. Volovich
%A V. N. Sushko
%T Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 211-231
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1971_9_2_a3/
%G ru
%F TMF_1971_9_2_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Self-interacting ferrhion field with a zero rest mass in two-dimensional space-time is investigated by methods of the so called constructive field theory. The renormalized Hamiltonian including cut-off formfactors and counter-terms of a definite structure and the Heisenberg field corresponding to this Hamiltonian are constructed. The space of physical particles is explicitly described, in which both the Hamiltonian and the Heisenberg field admit the removal of the ultraviolet eut-off. The Wightman functions corresponding to the local field obtained admit the removal of the spatial cut-off. The form of the counter-terms is found, with which the limit Wightman functions coincide with those constructed by Klaiber.

[1] J. Glimm, A. Jaffe, Phys. Rev., 176 (1968), 1945 ; Ann. Math., 91 (1970), 362 | DOI | MR | Zbl | DOI | MR | Zbl

[2] J. Cannon, A. Jaffe, Commun. Math. Phys., 17 (1970), 261 | DOI | MR | Zbl

[3] J. Glimm, A. Jaffe, Ann. Phys., 60 (1970), 321 ; J. Funct. Analysis (to appear) | DOI | MR | Zbl

[4] A. D. Sukhanov, ZhETF, 47 (1964), 1303 48, 538, 1965. | MR

[5] J. Glimm, Commun. Math. Phys., 10 (1968), 1 | DOI | MR | Zbl

[6] K. Osterwalder, Boson fields with the $\lambda\Phi^3$-interection in two, three and four dimensions

[7] K. Hepp, Systems a un nombre infini de degres de liberte, Springer-Verlag, 1970

[8] K. Fridrikhs, Vozmuschenie spektra operatorov v gilbertovom prostranstve, «Mir», 1969

[9] L. D. Faddeev, DAN SSSR, 152 (1963), 573 | MR

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

[11] K. Johnson, Nuovo Cim., 20 (1961), 773 | DOI | MR

[12] F. A. Berezin, Matem. sb., 76 (1968), 1 | MR

[13] A. S. Vaitman, Problemy v relyativistskoi dinamike kvantovannykh polei, «Nauka», 1968

[14] D. C. Mattis, E. H. Lieb, J. Math. Phys., 6 (1965), 304 | DOI | MR

[15] D. A. Uhlenbrock, Commun. Math. Phys., 4 (1967), 64 | DOI | MR | Zbl

[16] V. N. Likhachev, V. N. Sushko, Pisma ZhETF, 5 (1967), 376

[17] A. Theumann, J. Math. Phys., 8 (1967), 2460 | DOI

[18] B. Klaiber, Boulder Lectures of Theoretical Physics, 1967

[19] F. A. Berezin, Metod vtorichnogo kvantovaniya, «Nauka», 1965 | MR

[20] J. von Neumann, Comp. Math., 6 (1938), 1 | MR | Zbl

[21] O. I. Zavyalov, V. N. Sushko, TMF, 1 (1969), 153