v 1 7 O ct 1 99 6 The Polar Decomposition of q - Deformed
نویسنده
چکیده
In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite dimensional one when q is a root of unity. In this paper we use the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. The polar decomposition of an operator means that the operator can be written as a unitary times a hermitian operator.
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