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Low Energy Consequences of Loop Quantum Gravity

As the loop quantum gravity is based on polymer quantization, we will argue that the polymer length (like string length) can be several orders larger than the Planck length, and this can have low energy consequences. We will demonstrate that a short distance modification of a quantum system by polymer quantization and by string theoretical considerations can produce similar behavior. Moreover, it will be demonstrated that a family of different deformed Heisenberg algebras can produce similar low energy effects. We will analyze such polymer correction to a degenerate Fermi gases in a harmonic trap, and its polymer corrected thermodynamics.