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arXiv · 1712.05306

A new theorem on the representation structure of the $SL(2, \mathbb{C})$ group acting in the Hilbert space of the quantum Coulomb field

Jaroslaw Wawrzycki
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Abstract

Using the results obtained by Staruszkiewicz in Acta Phys. Pol. B 23, 591 (1992) and in Acta Phys. Pol. B 23, 927 (1992) we show that the representations acting in the eigenspaces of the total charge operator corresponding to the eigenvalues $n_1, n_2$ whose absolute values are less than or equal $\sqrt{\pi/e^2}$ are inequivalent if $|n_1| \neq |n_2|$ and contain the supplementary series component acting as a discrete component. On the other hand the representations acting in the eigenspaces corresponding to eigenvalues whose absolute values are greater than $\sqrt{\pi/e^2}$ are all unitarily equivalent and do not contain any supplementary series component.

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Jaroslaw Wawrzycki. 2017-12-14. A new theorem on the representation structure of the $SL(2, \mathbb{C})$ group acting in the Hilbert space of the quantum Coulomb field. https://doi.org/10.5506/aphyspolb.49.171

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