Geração das matrizes de spin de Pauli a partir dos vetores de Jones
Resumo
A partir do uso dos estados de polarização da luz representados por vetores de Jones que pertencem a um espaço vetorial linear complexo de uma dimensão, são elaboradas estruturas algébricas que são conhecidas como “díades” ou “tensores de segunda ordem” que, nesse caso, conformam um espaço vetorial complexo de duas dimensões. Com esses tensores de segunda ordem, que podem ser expressos de forma matricial, são construídas sequências de relações de comutação com alternância dos estados de polarização da luz. As sequências de relações de comutação, com a propriedade de alternância dada pela permutação dos estados de polarização da luz, são apresentadas como combinações lineares que geram de forma simples as matrizes de spin de Pauli. Os estados de polarização dos vetores de Jones utilizados para construir as sequências das relações de comutação das formas díades pertencem a formas de tipo circular, à esquerda e à direita ou linear. A transição de um espaço vetorial complexo, no qual os vetores de Jone agem, a um espaço vetorial linear complexo de duas dimensões, no qual a base deste último espaço é conformada pela matriz unidade e as matrizes de spin de Pauli, é factível por meio de relações de comutação e da utilização de vetores de Jones em estados de polarização linear e circular.
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