It has been argued by Valatin in 1951 that the exterior algebra is the natural
mathematical framework for the N-body problem of identical Fermionic particles [1].
However, the tools developed in this mathematical field [2] have remained little
exploited up to now in quantum physics. It is the purpose of this talk to review
some of the key exterior algebra concepts and techniques that we find particularly
relevant for physicists and chemists.

We will focus on the concept of p-internal space and the derived one of p-
orthogonality [3], which generalizes that of strong-orthogonality and can be viewed
as a graded indistinguishability measure for electronic states. p-orthogonality has
been applied in the past to constrain geminal models [4], and work in progress
shows that computational cost can be drastically reduced by using new geminal
ansätze based on such algebraic constraints.

Time permitting, we will show the connection between the concept of “cancelator
space” and Configuration Interactions with arbitrary reference wave functions.

References
[1] J. G. Valatin, Le Journal de Physique et le Radium 12, 131 (1951).
[2] P. Cassam-Chenaı̈, F. Patras, J. Math. Phys. 44, 4884-4906 (2003).
[3] P. Cassam-Chenaı̈, Phys. Rev. A77, 032103 (2008).
[4] P. Cassam-Chenaı̈, V. Rassolov, Chem. Phys. Lett. 487, 147-152 (2010).