Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 2, pp. 161-166
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A. N. Vasil'ev. Criterion for the commutant of a quantized field to be algebraically closed. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 2, pp. 161-166. http://geodesic.mathdoc.fr/item/TMF_1970_5_2_a0/
@article{TMF_1970_5_2_a0,
author = {A. N. Vasil'ev},
title = {Criterion for the commutant of a~quantized field to be algebraically closed},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {161--166},
year = {1970},
volume = {5},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1970_5_2_a0/}
}
TY - JOUR
AU - A. N. Vasil'ev
TI - Criterion for the commutant of a quantized field to be algebraically closed
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1970
SP - 161
EP - 166
VL - 5
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%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
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%F TMF_1970_5_2_a0
A necessary and sufficient condition is formulated for the commutant [4–5] of a given quantized field to be algebraically closed (i.e., closed with respect to algebraic operations). If the field satisfies the usual Wightman axions, the assumption that its commutant is a $^*$ algebra implies that this $^*$ algebra is abelian.
