We establish a general identity that expresses a Pfaffian of a certain matrix as a quotient of homogeneous polynomials. This identity arises in the study of weakly interacting many-body systems and its proof provides another way of realizing the equivalence of two proposed types of trial wave functions used to describe such systems. In the proof of our identity, we make use of only elementary linear algebra and combinatorics and thereby avoid use of more advanced conformal field theory in establishing the aforementioned equivalence.
Mulay, Shashikant B.; Quinn, John J.; and Shattuck, Mark A.
A Generalized Polynomial Identity Arising from Quantum Mechanics,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 5.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/5