Traço parcial em sistemas relativísticos: uma nova visão
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2013-11-08
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Universidade Federal de Goiás
Resumo
In this dissertation, the use of the partial trace of momentum degrees of freedom in
the construction of spin reduced density matrices for relativistic massive systems is analyzed. In the regime considered here, massive particles can be described by irreducible unitary representations of the Poincar e group, and the base states are labeled by the dynamical variables of momentum and spin. The reduced density matrices obtained by the partial trace of momenta have unusual properties, since they are not covariant under the action of restricted Lorentz transformations. That behavior produces some important consequences in the study of quantum information in relativistic systems. However, recent arguments have been presented against the use of those matrices in the description of processes involving the transfer of information stored in spin degrees of freedom of relativistic massive particles. Those criticisms are discussed in this dissertation and a connection with the structure of the space of states associated with a given unitary representation is established through a detailed study of the induced representation method applied to the Poincar e group. This allows rewriting the criticisms in literature without the need of a speci c model of interaction for the spin measurement. Besides that, the analysis performed here allows to establish a new method to construct e ective spin reduced density matrices. The presented approach allows recovering the results in the literature and, at the same time, to incorporate the criticisms in a consistent way. However, it is necessary to abandon the usual partial trace of the momentum degrees of freedom and the interpretation in the literature for the spin reduced density matrices. The examples presented in the arguments against the usual spin reduced density matrices are studied using the approach proposed in this dissertation.
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Citação
TAILLEBOIS, E. R. F. Traço parcial em sistemas relativísticos: uma nova visão. 2013. 85 f. Dissertação (Mestrado em Fisica) - Universidade Federal de Goiás, Goiânia, 2013.