Quantum field theory with non-Fock asymptotic fields: the existence of the $S$-matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 1, pp. 25-39
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We construct a family of relativistic-invariant generating functionals of the form $$F(f^*,g)=\exp\left\{\gamma\int\frac{d\mathbf k}{\omega(\mathbf k)}f^*(\mathbf k)g(\mathbf k)\right\}$$ for the non-Fock representations of the CCR. We analyze the first order in the coupling constant of the model theory. In this theory, the asymptotic in field coincides with the field $\varphi(x)$ corresponding to such a functional. We prove that in the first order, the in and out fields are unitarily equivalent and the scattering matrix consequently exists. Moreover, the kinematics of the “non-Fock quantum field theory” is much richer than the standard kinematics: in this case, the $S$-matrix does not coincide with the chronologically ordered exponent of the interaction Lagrangian.
@article{TMF_1999_121_1_a2,
author = {O. I. Zavialov and A. M. Malokostov},
title = {Quantum field theory with {non-Fock} asymptotic fields: the existence of the $S$-matrix},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {25--39},
publisher = {mathdoc},
volume = {121},
number = {1},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_1_a2/}
}
TY - JOUR AU - O. I. Zavialov AU - A. M. Malokostov TI - Quantum field theory with non-Fock asymptotic fields: the existence of the $S$-matrix JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1999 SP - 25 EP - 39 VL - 121 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1999_121_1_a2/ LA - ru ID - TMF_1999_121_1_a2 ER -
%0 Journal Article %A O. I. Zavialov %A A. M. Malokostov %T Quantum field theory with non-Fock asymptotic fields: the existence of the $S$-matrix %J Teoretičeskaâ i matematičeskaâ fizika %D 1999 %P 25-39 %V 121 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1999_121_1_a2/ %G ru %F TMF_1999_121_1_a2
O. I. Zavialov; A. M. Malokostov. Quantum field theory with non-Fock asymptotic fields: the existence of the $S$-matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 1, pp. 25-39. http://geodesic.mathdoc.fr/item/TMF_1999_121_1_a2/