One-dimensional polymer Fermi gas at zero temperature

In this work we study a completely degenerated fermion gas at zero temperature employing a semi-classical approximation obtained from polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity. These models allow the study in a simplified way of the discreteness of space present in loop quantum gravity. We obtain the thermodynamic quantities modified by the polymer scale and we note that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum p(F).