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arXiv · 1601.06424

Linear representations of SU(2) described by using Kravchuk polynomials

Nicolae Cotfas
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Abstract

We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it Kravchuk transform. Some of its properties are investigated and used in order to obtain a simple alternative description for the irreducible representations of the Lie algebra su(2) and group SU(2). Our approach offers a deeper insight into the structure of the linear representations of SU(2) and new possibilities of computation, very useful in applications in quantum mechanics, quantum information, signal and image processing.

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Nicolae Cotfas. 2016-02-17. Linear representations of SU(2) described by using Kravchuk polynomials. https://arxiv.org/abs/1601.06424

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