Geodesic
Formulas for functions of ordered operators
Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 267-277

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In an algebra with a lattice of functions of ordered elements (e.g., in an algebra of operators), we investigate the expansions of functions of the type $f(A+B)$ and $\varphi(\stackrel1A,\stackrel2B)$ in powers of the commutators $A$, $B$. In particular, we obtain all the terms of the expansion $$ f(A+B)=f(\stackrel1A+\stackrel2B)+\frac12\stackrel2{\overline{[A,B]}}f^{(2)}(\stackrel1A+\stackrel3B)+\dots $$ A diagram method for a similar type of calculation is developed. Our discussion is based on Maslov's technique of ordered operators. 
@article{MZM_1975_18_2_a12,
     author = {M. V. Karasev},
     title = {Formulas for functions of ordered operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {267--277},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a12/}
}
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M. V. Karasev. Formulas for functions of ordered operators. Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a12/