Relativistic-Geometric Entanglement: Symmetry Groups of Systems of Entangled Particles

Abstract

It is known that entangled particles involve Lorentz symmetry violation. Hence, we pay attention to Lorentz transformations of signature $(m,n)$ for all positive integers $m$ and $n$. We show that these form the symmetry groups by which systems of $m$ entangled $n$-dimensional particles can be understood, just as the common Lorentz group of signature $(1,3)$ forms the symmetry group by which Einstein's special theory of relativity is understood. A novel, unified parametric realization of the Lorentz transformations of any signature $(m,n)$ shakes down the underlying matrix algebra into elegant and transparent results.