Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Foundation of one-particle reduced density matrix functional theory for
  excited states   In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional
theory (RDMFT) has been proposed for calculating energies of selected
eigenstates of interacting many-fermion systems. Here, we develop a solid
foundation for this so-called $\boldsymbol{w}$-RDMFT and present the details of
various derivations. First, we explain how a generalization of the Ritz
variational principle to ensemble states with fixed weights $\boldsymbol{w}$ in
combination with the constrained search would lead to a universal functional of
the one-particle reduced density matrix. To turn this into a viable functional
theory, however, we also need to implement an exact convex relaxation. This
general procedure includes Valone's pioneering work on ground state RDMFT as
the special case $\boldsymbol{w}=(1,0,\ldots)$. Then, we work out in a
comprehensive manner a methodology for deriving a compact description of the
functional's domain. This leads to a hierarchy of generalized exclusion
principle constraints which we illustrate in great detail. By anticipating
their future pivotal role in functional theories and to keep our work
self-contained, several required concepts from convex analysis are introduced
and discussed.

33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph