The interactions we deal with in physics involve one or two particles and therefore are represented by one and two—particle operators. Some formalisms introduce more than two—particle operators. In general calculating matrix elements we would like to separate the physical information, the part that depends on the p-particle operator  and thus is expressed by the p-dimensional integrals $$\int {\phi _{{{{a}_{1}}}}^{*}{\mkern 1mu} \left( 1 \right) \ldots \phi _{{{{a}_{p}}}}^{*}{\mkern 1mu} \left( p \right)} {\mkern 1mu} \hat{A}\left( {1 \ldots p} \right){\mkern 1mu} {{\phi }_{{{{b}_{1}}}}}{\mkern 1mu} \left( 1 \right) \ldots {{\phi }_{{{{b}_{p}}}}}{\mkern 1mu} \left( p \right)d{{x}_{1}}..d{{x}_{p}}$$