Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-06-14
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
In order to investigate some of the physical consequences of the existence of a minimal length, we propose to include it in the framework of Quantum Mechanics by modifying the Heisenberg algebra, so that a minimum non-zero value for the uncertainty $\Delta x$ emerges, which, being a limitation to the localizability of particles, plays the desired role of a \emph{minimal length}. The Hilbert space of the theory must be modified accordingly, and the changes are not merely quantitative. On the contrary, our main result is that the familiar concept of "position measurement" must be reformulated, as well as other concepts related to it, and we present a proposal for such reformulation. We also calculate the Casimir force resulting from the proposed algebra.
Dorsch Glauber
Nogueira Jose Alexandre
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