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

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