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 TMF, 1971, Volume 9, Number 2, Pages 211–231 (Mi tmf4453)

Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field

I. V. Volovich, V. N. Sushko

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1971, 9:2, 1086–1100

Citation: I. V. Volovich, V. N. Sushko, “Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field”, TMF, 9:2 (1971), 211–231; Theoret. and Math. Phys., 9:2 (1971), 1086–1100

Citation in format AMSBIB
\Bibitem{VolSus71} \by I.~V.~Volovich, V.~N.~Sushko \paper Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I.~Local field \jour TMF \yr 1971 \vol 9 \issue 2 \pages 211--231 \mathnet{http://mi.mathnet.ru/tmf4453} \transl \jour Theoret. and Math. Phys. \yr 1971 \vol 9 \issue 2 \pages 1086--1100 \crossref{https://doi.org/10.1007/BF01036945} 

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This publication is cited in the following articles:
1. I. Ya. Aref'eva, “Renormalized scattering theory for Yukawa model II. Wave operators”, Theoret. and Math. Phys., 15:2 (1973), 467–476
2. A. K. Pogrebkov, “Thirring model. Asymptotic fields and $S$ matrix $\pm2\pi\surd{\overline{2n}}$, $n=0,1,2,…$”, Theoret. and Math. Phys., 17:1 (1973), 977–983
3. A. K. Pogrebkov, V. N. Sushko, “Hamiltonian theory of the interaction of a massive vector field with a massless fermion field in two-dimensional spacetime: The $(\tilde\Psi\gamma^{\mu}\Psi B_{\mu})_2$ interaction”, Theoret. and Math. Phys., 22:2 (1975), 110–122
4. A. K. Pogrebkov, V. N. Sushko, “Quantization of the $(\sin\varphi)_2$ interaction in terms of fermion variables”, Theoret. and Math. Phys., 24:3 (1975), 935–937
5. A. K. Pogrebkov, V. N. Sushko, “Quantum solitons and their connection with fermion fields for the $(\sin\varphi)_2$”, Theoret. and Math. Phys., 26:3 (1976), 286–289
6. V. N. Sushko, “Fermionization of the $(\sin\varphi)_2$ interaction in a box”, Theoret. and Math. Phys., 37:2 (1978), 949–969
7. D. Ts. Stoyanov, L. K. Khadzhiivanov, “Theory of Wightman functions in the thirring model”, Theoret. and Math. Phys., 46:3 (1981), 236–242
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