Some Formulas for Invariant Phases of Unitary Matrices by Jarlskog

TL;DR

This paper details calculations of Jarlskog's determinant for 3x3 and 4x4 matrices and explores formulas for invariant phases of unitary matrices, deriving explicit relations among them.

Contribution

It provides detailed calculations and new explicit relations for invariant phases of unitary matrices, extending previous work on Jarlskog's determinant.

Findings

Calculated Jarlskog's determinant for n=3,4

Derived explicit relations for invariant phases

Enhanced understanding of unitary matrix invariants

Abstract

We describe calculations of Jarlskog's determinant in the case of n=3,4 in detail. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations of them.