Quantum Mechanics on Periodic and Non-Periodic Lattices and Almost Unitary Schwinger Operators

TL;DR

This paper explores the mathematical structure of Schwinger algebra and introduces almost unitary Schwinger operators derived from translation operators on finite lattices, establishing their equivalence and new representations.

Contribution

It presents a novel formulation of Schwinger operators on finite lattices and demonstrates their algebraic equivalence, expanding the mathematical framework of quantum lattice systems.

Findings

Almost unitary Schwinger operators are equivalent to the traditional Schwinger algebra.

New representations for MN(C) are introduced using these operators.

Mathematical relations between different algebraic structures are established.

Abstract

In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations between these algebras and show that the almost unitary Schwinger operators are equivalent to the Schwinger algebra. We introduce new representations for MN(C) in terms of these algebras.