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We explore the conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories. If the potential in noncommutative quantum mechanics is chosen as V=Ωℵ with ℵ defined in the text, then for the value [Formula: see text] (which measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find different values for [Formula: see text] and, therefore, the possible bounds for [Formula: see text] should be searched in a physical independent scenario. This last fact could explain the different bounds for [Formula: see text] found in the literature.

We compute the critical temperature for the chiral transition in the background of a magnetic field in the linear sigma model, including the quark contribution and the thermo-magnetic effects induced on the coupling constants at one loop level. We show that the critical temperature decreases as a function of the field strength. The effect of fermions on the critical temperature is small and the main effect on this observable comes from the charged pions. The findings support the idea that the anticatalysis phenomenon receives a contribution due only to quiral symmetry effects independent of the deconfinement transition.Comment: 8 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1406.3885. Accepted for publication in Phys. Rev.

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound θ ∼ [10 TeV] −2 is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov-Bohm effect is also discussed.

The density corrections, in terms of the isospin chemical potential µ I , to the mass of the pions are studied in the framework of the SU (2) low energy effective chiral lagrangian. The pion decay constant f π (T, µ I ) is also analized. As a function of temperature for µ I = 0, the mass remains quite stable, starting to grow for very high values of T , confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the π ± should condensate when µ I = ∓m π . This is not longer valid anymore at finite T . The mass of the π 0 acquires also a non trivial dependence on µ I due to the finite temperature.

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We compute the one-loop thermomagnetic corrections to the self-coupling in a model where charged scalars interact also with a constant magnetic field. The calculation is motivated by the possibility that the critical temperature for the chiral phase transition in a magnetic background can be influenced by the dependence of the coupling constant on the magnetic field. We show that the coupling decreases as a function of the field strength. This functional dependence introduces in turn a correction to the boson masses which causes the critical temperature to decrease as a function of the field strength.

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