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Polymer quantum effects on compact stars models

In this work we study a completely degenerated fermion gas at zero temperature within a semiclassical approximation for the Hamiltonian arising in polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity that allow the study of the discreteness of space and other features of the loop quantization in a simplified way. We obtain the polymer modified thermodynamical properties noticing that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum $p_F$. We also obtain the corresponding expansion of thermodynamical variables for small values of the polymer length scale $λ$. With this results we study a simple model of a compact object where the gravitational collapse is supported by electron degeneracy pressure. We find polymer corrections to the mass of the star. When compared with typical measurements of the mass of white dwarfs we obtain a bound on the polymer length of $λ^2\lesssim 10^{-26}m^2$.