Higher Dimensional Multiparameter Unitary and Nonunitary Braid Matrices: Even Dimensions

TL;DR

This paper introduces a new class of high-dimensional multiparameter braid matrices that depend on multiple parameters, unifying unitary and nonunitary solutions across even dimensions, with potential applications in quantum computing and mathematical physics.

Contribution

It presents a comprehensive construction of $(2n)^2$-dimensional multiparameter braid matrices for all $n \,\geq\, 1$, unifying unitary and nonunitary cases.

Findings

Matrices depend on $2n^2$ free parameters.

Real parameters yield nonunitary matrices.

Imaginary parameters produce unitary matrices.

Abstract

A class of $(2n)^2\times(2n)^2$ multiparameter braid matrices are presented for all $n$ $(n\geq 1)$. Apart from the spectral parameter $\theta$, they depend on $2n^2$ free parameters $m_{ij}^{(\pm)}$, $i,j=1,...,n$. For real parameters the matrices $R(\theta)$ are nonunitary. For purely imaginary parameters they became unitary. Thus a unification is achieved with odd dimensional multiparameter solutions presented before.