Abstract
At a fundamental level the notion of particle (quantum) comes from quantum field theory. From this point of view we estimate corrections to the free particle wave function due to minimum-length deformed quantum mechanics to the first order in the deformation parameter. Namely, in the matrix element that in the standard case sets the free particle wave function there appear three kinds of corrections when the field operator is calculated by using the minimum-length deformed quantum mechanics. Starting from the standard (not modified at the classical level) Lagrangian, after the field quantization we get a modified dispersion relation, and besides that we find that the particle’s wave function contains a small fraction of an antiparticle wave function and the backscattered wave. The result leads to interesting implications for black hole physics.
- Received 14 October 2010
DOI:https://doi.org/10.1103/PhysRevD.84.044043
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