Generalization of the Bloch-Messiah-Zumino theorem
J. Dobaczewski
TL;DR
This paper presents a method to construct a basis where two complex antisymmetric matrices simultaneously take canonical forms, regardless of properties of their product, with applications to many-fermion systems.
Contribution
It introduces a general construction for canonical forms of two arbitrary complex antisymmetric matrices without restrictions on their product.
Findings
Canonical bases for complex antisymmetric matrices are constructed.
The method applies to generator-coordinate-method in many-fermion systems.
No restrictions on the properties of the matrix product are required.
Abstract
It is shown how to construct a basis in which two arbitrary complex antisymmetric matrices C and C' acquire simultaneously canonical forms. The present construction is not restricted by any conditions on properties of the C^+C' matrix. Canonical bases pertaining to the generator-coordinate-method treatment of many-fermion systems are discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.