Abstract
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral
representations of operators, is actively progressing in electronic structure theory (mostly on the
independent-particle level and, recently, second-order perturbation theory), the concepts of
multiresolution and adaptivity can also be utilized within the traditional formulation of correlated
(many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal)
tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra
(SATA) which exploits an adaptive representation of tensors of many-body operators via the local
adjustment of the basis set quality. Given a series of locally supported fragment bases of a
progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with
adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability
and reliability of local correlated many-body methods of electronic structure theory, especially those
directly based on atomic orbitals (or any other localized basis functions).