  As a new approach to efficiently describe correlation effects in the
relativistic quantum world we propose to consider reduced density matrix
functional theory, where the key quantity is the first-order reduced density
matrix (1-RDM). In this work, we first introduce the theoretical foundations to
extend the applicability of this theory to the relativistic domain. Then, using
the so-called no-pair (np) approximation, we arrive at an approximate treatment
of the relativistic effects by focusing on electronic wavefunctions and
neglecting explicit contributions from positrons. Within the np approximation
the theory becomes similar to the nonrelativistic case, with as unknown only
the functional that describes the electron-electron interactions in terms of
the 1-RDM. This requires the construction of functional approximations, and we
therefore also present the relativistic versions of some common RDMFT
approximations that are used in the nonrelativistic context and discuss their
properties
