Maximally localized states and causality in non commutative quantum theories

We give simple representations for quantum theories in which the position commutators are non vanishing constants. A particular representation reproduces results found using the Moyal star product. The notion of exact localization being meaningless in these theories, we adapt the notion of ``maximally localized states'' developed in another context . We find that gaussian functions play this role in a 2+1 dimensional model in which the non commutation relations concern positions only. An interpretation of the wave function in this non commutative geometry is suggested. We also analyze higher dimensional cases. A possible incidence on the causality issue for a Q.F.T with a non commuting time is sketched.Comment: 11 pages, Revtex. The presentation has been improved, the subsection on high dimensions has been modified. This version will appear in PR

Ultraviolet cut off, black hole-radiation equilibrium and big bang

In the presence of a minimal uncertainty in length, there exists a critical temperature above which the thermodynamics of a gas of radiation changes drastically. We find that the equilibrium temperature of a system composed of a Schwarzschild black hole surrounded by radiation is unaffected by these modifications. This is in agreement with works related to the robustness of the Hawking evaporation. The only change the deformation introduces concerns the critical volume at which the system ceases to be stable. On the contrary, the evolution of the very early universe is sensitive to the new behavior. We readdress the shortcomings of the standard big bang model(flatness, entropy and horizon problems) in this context, assuming a minimal coupling to general relativity. Although they are not solved, some qualitative differences set in.Comment: 10 pages revtex, 1 figur

The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection

On the fuzzy sphere, no state saturates simultaneously all the Heisenberg uncertainties. We propose a weaker uncertainty for which this holds. The family of states so obtained is physically motivated because it encodes information about positions in this fuzzy context. In particular, these states realize in a natural way a deformation of the stereographic projection. Surprisingly, in the large $j$ limit, they reproduce some properties of the ordinary coherent states on the non commutative plane.Comment: 18 pages, Latex. Minor changes in notations. Version to appear in JHE

Quantum mechanics on non commutative spaces and squeezed states: a functional approach

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and the commutators in these theories generically leads to a harmonic oscillator whose positions and momenta mean values are not strictly equal to the ones predicted by classical mechanics. This raises the question of the nature of quasi classical states in these models. We propose an extension based on a variational principle. The action considered is the sum of the absolute values of the expressions associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory i.e we recover the known Gaussian functions. Besides them, we find other states which can be expressed as products of Gaussians with specific hyper geometrics. We illustrate our construction in two models defined on a four dimensional phase space: a model endowed with a minimal length uncertainty and the non commutative plane. Our proposal leads to second order partial differential equations. We find analytical solutions in specific cases. We briefly discuss how our proposal may be applied to the fuzzy sphere and analyze its shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and misprints have been corrected. Version to appear in JHE

Inhibition of Autophagy Signaling via 3-methyladenine Rescued Nicotine-Mediated Cardiac Pathological Effects and Heart Dysfunctions.

Rationale: Cigarette smoking is a well-established risk factor for myocardial infarction and sudden cardiac death. The deleterious effects are mainly due to nicotine, but the mechanisms involved and theranostics remain unclear. Thus, we tested the hypothesis that nicotine exposure increases the heart sensitivity to ischemia/reperfusion injury and dysfunction, which can be rescued by autophagy inhibitor. Methods: Nicotine or saline was administered to adult rats via subcutaneous osmotic minipumps in the absence or presence of an autophagy inhibitor, 3-methyladenine (3-MA). After 30 days of nicotine treatment, the rats underwent the cardiac ischemia/reperfusion (I/R) procedure and echocardiography analysis, and the heart tissues were isolated for molecular biological studies. Results: Nicotine exposure increased I/R-induced cardiac injury and cardiac dysfunction as compared to the control. The levels of autophagy-related proteins including LC3 II, P62, Beclin1, and Atg5 were upregulated in the reperfused hearts isolated from nicotine-treated group. In addition, nicotine enhanced cardiac and plasma ROS production, and increased the phosphorylation of GSK3β (ser9) in the left ventricle tissues. Treatment with 3-MA abolished nicotine-mediated increase in the levels of autophagy-related proteins and phosphorylation of GSK3β, but had no effect on ROS production. Of importance, 3-MA ameliorated the augmented I/R-induced cardiac injury and dysfunction in the nicotine-treated group as compared to the control. Conclusion: Our results demonstrate that nicotine exposure enhances autophagy signaling pathway, resulting in development of ischemic-sensitive phenotype of heart. It suggests a potentially novel therapeutic strategy of autophagy inhibition for the treatment of ischemic heart disease

A Brane model with two asymptotic regions

Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip.S.Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.Comment: 9 pages revtex, 4 figures,version to appear in PR