Matrix Theory

Djordje Minić

Matrix String Theory of Banks, Fischler, Shenker and Susskind can be understood as a generalized quantum theory (provisionally named "quansical" theory) which differs from Adler's generalized trace quantum dynamics. The effective Matrix String Theory Hamiltonian is constructed in a particular fermionic realization of Matrix String Theory treated as an example of "quansical" theory.

Henry Pierce Stapp

Gary E. Bowman

Kazuo Takayanagi

We present the biorthogonal complement of the standing wave state and its relation to scattering operators. This establishes a completeness relation in terms of the standing wave states, and therefore completes the $\mathit{R}$-matrix (reactance matrix) theory of scattering. We clarify with an example that the $\mathit{R}$-matrix theory, in its formulation presented here, can claim its due place in addition to the standard $\mathit{T}$-matrix theory.

Eduardo V. Ludeña, Fernando Javier Torres, Cesar Costa

The N-representability conditions on the reduced second-order reduced density matrix (2-RDM), impose restrictions not only in the context of reduced density matrix theory (RDMT), but also on functionals advanced in one-matrix theory such as natural orbital functional theory (NOFT), and on functionals depending on the one-electron density such as those of density functional theory (DFT). We review some aspects of the applications of these N-representability conditions in these theories and present some conclusions.