Geodesic
On field algebras in quantum theory with indefinite metric
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 1, pp. 57-77

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The paper consists of two parts. The first discusses the problem of formulating the algebraic approach directly in a space with indefinite metric. One of the possible ways of constructing a net of local field algebras $\mathscr F(O)$ in the $J$ space (Krein space) is considered; it is based on the Bisognano–Wichmann formalism. The second part establishes a number of properties of "$WJ^*$ algebras" (weakly closed algebras with $J$ involution and unit in the $J$ space); the algebras $\mathscr F(O)$ belong to this class. The methods of the proof use generalizations of the fundamental concepts of Tomita–Takesaki theory for algebras with $J$ involution. 
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     author = {K. Yu. Dadashyan and S. S. Horuzhy},
     title = {On field algebras in quantum theory with indefinite metric},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {57--77},
     publisher = {mathdoc},
     volume = {54},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_1_a5/}
}
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K. Yu. Dadashyan; S. S. Horuzhy. On field algebras in quantum theory with indefinite metric. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 1, pp. 57-77. http://geodesic.mathdoc.fr/item/TMF_1983_54_1_a5/