Two-point functions of local infinite-component fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 2, pp. 153-182
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An explicitly covariant technique is used to derive a representation for the two-point function
$F_{\varphi\psi}(x-y)=\langle0|\varphi(x)\psi(y)|0\rangle$ which takes into account Lorentz covariance, the spectralcondition, and locality; the fields $\varphi$ and $\psi$ may transform in accordance with arbitrary irreducible representations of the proper Lorentz group. The method can also be applied to local nonrenormalizable theories (in which the two-point functions in momentum space may have a growth faster than polynomial). As a corollary it is proved (without any “technical assumptions”) that the mass spectrum in a theory of local infinite-component fields is infinitely degenerate with respect to the spin. By the same token, the well-known Grodsky–Streater “no-go” theorem is extended to nonrenormalizable theories.
@article{TMF_1971_7_2_a0,
author = {A. I. Oksak and I. T. Todorov},
title = {Two-point functions of local infinite-component fields},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {153--182},
publisher = {mathdoc},
volume = {7},
number = {2},
year = {1971},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1971_7_2_a0/}
}
A. I. Oksak; I. T. Todorov. Two-point functions of local infinite-component fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 2, pp. 153-182. http://geodesic.mathdoc.fr/item/TMF_1971_7_2_a0/