ON FAITHFUL MATRIX REPRESENTATIONS OF $q$-DEFORMED LIE ALGEBRA FOR COUPLED QUANTIZED OSCILLATORS

Abstract

The polynomially deformed Lie algebra, lq : [K0,K+]q = G (K+), [K−,K0]q = G (K−) , [K+,K−]q = P (K0), is introduced as a generalized model of the coupled quantized oscillators model, where G and P are real polynomial functions, subject to the physical properties: K0 is a real diagonal operator, and K− = K † +. Matrix representations are discussed and conditions are given for G and P to guarantee the existence of the faithful representations. AMS Subject Classification: 17B10, 17B81